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                       Semantic Analysis of SPARK Text
                             Examiner GPL Edition

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SPARK Simplifier GPL 2012
Copyright (C) 2012 Altran Praxis Limited, Bath, U.K.

function Parser_Utilities.convertIpv4






@@@@@@@@@@  VC: function_convertipv4_1.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
***  Proved C1:  begidx >= rr_type__linelengthindex__first
     using hypothesis H2.
***  Proved C2:  begidx <= rr_type__linelengthindex__last
     using hypothesis H3.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_2.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_3.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_4.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
***  Proved C1:  0 >= natural__first
     using hypothesis H8.
***  Proved C2:  0 <= natural__last
     using hypothesis H9.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_5.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
***  Proved C1:  0 >= unsigned_types__unsigned32__first
     using hypothesis H10.
***  Proved C2:  0 <= unsigned_types__unsigned32__last
     using hypothesis H11.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_6.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
***  Proved C1:  begidx < endidx
     using hypothesis H24.
***  Proved C2:  0 <= req_num_separators
     using hypothesis H25.
***  Proved C3:  0 <= max_digits_per_byte
     using hypothesis H27.
***  Proved C4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
     using hypothesis H1.
***  Proved C5:  begidx >= rr_type__linelengthindex__first
     using hypothesis H2.
***  Proved C6:  begidx <= rr_type__linelengthindex__last
     using hypothesis H3.
***  Proved C7:  endidx >= rr_type__linelengthindex__first
     using hypothesis H4.
***  Proved C8:  endidx <= rr_type__linelengthindex__last
     using hypothesis H5.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_7.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as H2)
          .
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
***  Proved C1:  ctr + 1 < endidx
     using hypothesis H41.
***  Proved C2:  numseparators <= req_num_separators
     using hypothesis H2.
***  Proved C3:  numdigitsinbyte + 1 <= max_digits_per_byte
     using hypothesis H44.
***  Proved C4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
     using hypothesis H4.
***  Proved C5:  begidx >= rr_type__linelengthindex__first
     using hypothesis H5.
***  Proved C6:  begidx <= rr_type__linelengthindex__last
     using hypothesis H6.
***  Proved C7:  endidx >= rr_type__linelengthindex__first
     using hypothesis H7.
***  Proved C8:  endidx <= rr_type__linelengthindex__last
     using hypothesis H8.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_8.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
***  Proved C1:  ctr + 1 < endidx
     using hypothesis H49.
***  Proved C2:  numseparators + 1 <= req_num_separators
     using hypothesis H50.
***  Proved C3:  0 <= max_digits_per_byte
     using hypothesis H52.
***  Proved C4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
     using hypothesis H4.
***  Proved C5:  begidx >= rr_type__linelengthindex__first
     using hypothesis H5.
***  Proved C6:  begidx <= rr_type__linelengthindex__last
     using hypothesis H6.
***  Proved C7:  endidx >= rr_type__linelengthindex__first
     using hypothesis H7.
***  Proved C8:  endidx <= rr_type__linelengthindex__last
     using hypothesis H8.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_9.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
***  Proved C1:  element(s, [ctr]) >= character__first
     using hypotheses H4, H9 & H10.
***  Proved C2:  element(s, [ctr]) <= character__last
     using hypotheses H4, H9 & H10.
***  Proved C3:  ctr >= rr_type__linelengthindex__first
     using hypothesis H9.
***  Proved C4:  ctr <= rr_type__linelengthindex__last
     using hypothesis H10.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_10.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
***  Proved C3:  ctr >= rr_type__linelengthindex__first
     using hypothesis H9.
***  Proved C4:  ctr <= rr_type__linelengthindex__last
     using hypothesis H10.
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H19:  bytetotal >= 0
<S>  New C1:  (ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus + 
          (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H20:  bytetotal <= 4294967295
<S>  New C2:  (ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus + 
          (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
-S-  Applied substitution rule convertipv4_rules(3).
     This was achieved by replacing all occurrences of req_num_separators by:
          3.
<S>  New H2:  numseparators <= 3
-S-  Applied substitution rule convertipv4_rules(5).
     This was achieved by replacing all occurrences of max_digits_per_byte by:
          3.
<S>  New H3:  numdigitsinbyte <= 3
-S-  Applied substitution rule convertipv4_rules(6).
     This was achieved by replacing all occurrences of ipv4_radix by:
          10.
<S>  New C1:  (10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C2:  (10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
-S-  Applied substitution rule convertipv4_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= character__last)
<S>  New H11:  element(s, [ctr]) >= 0
-S-  Applied substitution rule convertipv4_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  element(s, [ctr]) <= 255
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(32).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New C1:  (10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 
          4294967296) mod 4294967296 >= 0
<S>  New C2:  (10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 
          4294967296) mod 4294967296 <= 4294967295
-S-  Applied substitution rule convertipv4_rules(34).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H5:  begidx >= 1
<S>  New H7:  endidx >= 1
<S>  New H9:  ctr >= 1
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(35).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H6:  begidx <= 256
<S>  New H8:  endidx <= 256
<S>  New H10:  ctr <= 256
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
***  Proved C1:  (10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 
          4294967296) mod 4294967296 >= 0
***  Proved C2:  (10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 
          4294967296) mod 4294967296 <= 4294967295
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_11.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
***  Proved C1:  numdigitsinbyte + 1 >= natural__first
     using hypothesis H25.
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H26:  numdigitsinbyte <= 2147483647
<S>  New C2:  numdigitsinbyte <= 2147483646
-S-  Applied substitution rule convertipv4_rules(3).
     This was achieved by replacing all occurrences of req_num_separators by:
          3.
<S>  New H2:  numseparators <= 3
-S-  Applied substitution rule convertipv4_rules(5).
     This was achieved by replacing all occurrences of max_digits_per_byte by:
          3.
<S>  New H3:  numdigitsinbyte <= 3
-S-  Applied substitution rule convertipv4_rules(6).
     This was achieved by replacing all occurrences of ipv4_radix by:
          10.
<S>  New H21:  (10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
<S>  New H22:  (10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
-S-  Applied substitution rule convertipv4_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= character__last)
<S>  New H11:  element(s, [ctr]) >= 0
-S-  Applied substitution rule convertipv4_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  element(s, [ctr]) <= 255
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H25:  numdigitsinbyte >= 0
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H19:  bytetotal >= 0
<S>  New H21:  (10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H20:  bytetotal <= 4294967295
<S>  New H22:  (10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
-S-  Applied substitution rule convertipv4_rules(32).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H21:  (10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 
          4294967296) mod 4294967296 >= 0
<S>  New H22:  (10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 
          4294967296) mod 4294967296 <= 4294967295
-S-  Applied substitution rule convertipv4_rules(34).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H5:  begidx >= 1
<S>  New H7:  endidx >= 1
<S>  New H9:  ctr >= 1
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(35).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H6:  begidx <= 256
<S>  New H8:  endidx <= 256
<S>  New H10:  ctr <= 256
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
***  Proved C2:  numdigitsinbyte <= 2147483646
     using hypothesis H3.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_12.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
***  Proved C1:  numseparators + 1 >= natural__first
     using hypothesis H17.
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H18:  numseparators <= 2147483647
<S>  New C2:  numseparators <= 2147483646
-S-  Applied substitution rule convertipv4_rules(3).
     This was achieved by replacing all occurrences of req_num_separators by:
          3.
<S>  New H2:  numseparators <= 3
-S-  Applied substitution rule convertipv4_rules(5).
     This was achieved by replacing all occurrences of max_digits_per_byte by:
          3.
<S>  New H3:  numdigitsinbyte <= 3
-S-  Applied substitution rule convertipv4_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= character__last)
<S>  New H11:  element(s, [ctr]) >= 0
-S-  Applied substitution rule convertipv4_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  element(s, [ctr]) <= 255
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H17:  numseparators >= 0
-S-  Applied substitution rule convertipv4_rules(34).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H5:  begidx >= 1
<S>  New H7:  endidx >= 1
<S>  New H9:  ctr >= 1
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(35).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H6:  begidx <= 256
<S>  New H8:  endidx <= 256
<S>  New H10:  ctr <= 256
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
***  Proved C2:  numseparators <= 2147483646
     using hypothesis H2.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_13.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
***  Proved C1:  ctr >= rr_type__linelengthindex__first
     using hypothesis H9.
***  Proved C2:  ctr <= rr_type__linelengthindex__last
     using hypothesis H10.
-S-  Applied substitution rule convertipv4_rules(39).
     This was achieved by replacing all occurrences of 
          separatorindextype__first by:
          1.
<S>  New C3:  numseparators >= 0
-S-  Applied substitution rule convertipv4_rules(40).
     This was achieved by replacing all occurrences of separatorindextype__last 
          by:
          4.
<S>  New C4:  numseparators <= 3
-S-  Applied substitution rule convertipv4_rules(3).
     This was achieved by replacing all occurrences of req_num_separators by:
          3.
<S>  New H2:  numseparators <= 3
-S-  Applied substitution rule convertipv4_rules(5).
     This was achieved by replacing all occurrences of max_digits_per_byte by:
          3.
<S>  New H3:  numdigitsinbyte <= 3
-S-  Applied substitution rule convertipv4_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= character__last)
<S>  New H11:  element(s, [ctr]) >= 0
-S-  Applied substitution rule convertipv4_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  element(s, [ctr]) <= 255
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H17:  numseparators >= 0
<S>  New H19:  numseparators >= - 1
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H18:  numseparators <= 2147483647
<S>  New H20:  numseparators <= 2147483646
-S-  Applied substitution rule convertipv4_rules(34).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H5:  begidx >= 1
<S>  New H7:  endidx >= 1
<S>  New H9:  ctr >= 1
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(35).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H6:  begidx <= 256
<S>  New H8:  endidx <= 256
<S>  New H10:  ctr <= 256
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
***  Proved C3:  numseparators >= 0
     using hypothesis H17.
***  Proved C4:  numseparators <= 3
     using hypothesis H2.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_14.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  bytetotal >= 0
<S>  New H29:  grandtotal >= 0
<S>  New C1:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H28:  bytetotal <= 4294967295
<S>  New H30:  grandtotal <= 4294967295
<S>  New C2:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
-S-  Applied substitution rule convertipv4_rules(3).
     This was achieved by replacing all occurrences of req_num_separators by:
          3.
<S>  New H2:  numseparators <= 3
-S-  Applied substitution rule convertipv4_rules(4).
     This was achieved by replacing all occurrences of max_byte_value by:
          255.
<S>  New C1:  (256 mod unsigned_types__unsigned32__modulus * grandtotal mod 
          unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C2:  (256 mod unsigned_types__unsigned32__modulus * grandtotal mod 
          unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
-S-  Applied substitution rule convertipv4_rules(5).
     This was achieved by replacing all occurrences of max_digits_per_byte by:
          3.
<S>  New H3:  numdigitsinbyte <= 3
-S-  Applied substitution rule convertipv4_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= character__last)
<S>  New H11:  element(s, [ctr]) >= 0
-S-  Applied substitution rule convertipv4_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  element(s, [ctr]) <= 255
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H17:  numseparators >= 0
<S>  New H19:  numseparators >= - 1
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H18:  numseparators <= 2147483647
<S>  New H20:  numseparators <= 2147483646
-S-  Applied substitution rule convertipv4_rules(32).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New C1:  (256 * grandtotal mod 4294967296 + bytetotal) mod 4294967296 >= 0
<S>  New C2:  (256 * grandtotal mod 4294967296 + bytetotal) mod 4294967296 <= 
          4294967295
-S-  Applied substitution rule convertipv4_rules(34).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H5:  begidx >= 1
<S>  New H7:  endidx >= 1
<S>  New H9:  ctr >= 1
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(35).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H6:  begidx <= 256
<S>  New H8:  endidx <= 256
<S>  New H10:  ctr <= 256
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(39).
     This was achieved by replacing all occurrences of 
          separatorindextype__first by:
          1.
<S>  New H25:  numseparators >= 0
-S-  Applied substitution rule convertipv4_rules(40).
     This was achieved by replacing all occurrences of separatorindextype__last 
          by:
          4.
<S>  New H26:  numseparators <= 3
***  Proved C1:  (256 * grandtotal mod 4294967296 + bytetotal) mod 4294967296 
          >= 0
***  Proved C2:  (256 * grandtotal mod 4294967296 + bytetotal) mod 4294967296 
          <= 4294967295
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_15.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  bytetotal >= 0
<S>  New H29:  grandtotal >= 0
<S>  New H31:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H28:  bytetotal <= 4294967295
<S>  New H30:  grandtotal <= 4294967295
<S>  New H32:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_16.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H17:  numseparators >= 0
<S>  New H19:  numseparators >= - 1
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H18:  numseparators <= 2147483647
<S>  New H20:  numseparators <= 2147483646
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_17.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
***  Proved C1:  ctr + 1 >= rr_type__linelengthindex__first
     using hypothesis H9.
-S-  Applied substitution rule convertipv4_rules(35).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= 256 -> character__first <= element(s, [i___1]) and 
          element(s, [i___1]) <= character__last)
<S>  New H6:  begidx <= 256
<S>  New H8:  endidx <= 256
<S>  New H10:  ctr <= 256
<S>  New C2:  ctr <= 255
***  Proved C2:  ctr <= 255
     using hypotheses H1 & H8.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_18.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
***  Proved C1:  ctr + 1 >= rr_type__linelengthindex__first
     using hypothesis H9.
-S-  Applied substitution rule convertipv4_rules(35).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= 256 -> character__first <= element(s, [i___1]) and 
          element(s, [i___1]) <= character__last)
<S>  New H6:  begidx <= 256
<S>  New H8:  endidx <= 256
<S>  New H10:  ctr <= 256
<S>  New C2:  ctr <= 255
***  Proved C2:  ctr <= 255
     using hypotheses H1 & H8.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_19.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
***  Proved C1:  element(s, [begidx]) >= character__first
     using hypotheses H1, H2 & H3.
***  Proved C2:  element(s, [begidx]) <= character__last
     using hypotheses H1, H2 & H3.
***  Proved C3:  begidx >= rr_type__linelengthindex__first
     using hypothesis H2.
***  Proved C4:  begidx <= rr_type__linelengthindex__last
     using hypothesis H3.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_20.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H32).
***  Proved C1:  element(s, [ctr + 1]) >= character__first
     using hypotheses H4, H31 & H32.
***  Proved C2:  element(s, [ctr + 1]) <= character__last
     using hypotheses H4, H31 & H32.
***  Proved C3:  ctr + 1 >= rr_type__linelengthindex__first
     using hypothesis H31.
***  Proved C4:  ctr + 1 <= rr_type__linelengthindex__last
     using hypothesis H32.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_21.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H40).
***  Proved C1:  element(s, [ctr + 1]) >= character__first
     using hypotheses H4, H39 & H40.
***  Proved C2:  element(s, [ctr + 1]) <= character__last
     using hypotheses H4, H39 & H40.
***  Proved C3:  ctr + 1 >= rr_type__linelengthindex__first
     using hypothesis H39.
***  Proved C4:  ctr + 1 <= rr_type__linelengthindex__last
     using hypothesis H40.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_22.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H36 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H11).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [begidx]
          ) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [begidx]
          ) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
***  Proved C3:  begidx >= rr_type__linelengthindex__first
     using hypothesis H2.
***  Proved C4:  begidx <= rr_type__linelengthindex__last
     using hypothesis H3.
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  true
<S>  New C1:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [begidx])
           - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  true
<S>  New C2:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [begidx])
           - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
>>>  Restructured hypothesis H24 into:
     >>>  H24:  endidx <= begidx or (req_num_separators < 0 or (max_byte_value 
          < 0 or max_digits_per_byte < 0))
-S-  Applied substitution rule convertipv4_rules(3).
     This was achieved by replacing all occurrences of req_num_separators by:
          3.
<S>  New H24:  endidx <= begidx or (max_byte_value < 0 or max_digits_per_byte < 
          0)
-S-  Applied substitution rule convertipv4_rules(4).
     This was achieved by replacing all occurrences of max_byte_value by:
          255.
<S>  New H24:  endidx <= begidx or max_digits_per_byte < 0
-S-  Applied substitution rule convertipv4_rules(5).
     This was achieved by replacing all occurrences of max_digits_per_byte by:
          3.
<S>  New H24:  endidx <= begidx
-S-  Applied substitution rule convertipv4_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= character__last)
<S>  New H30:  element(s, [begidx]) >= 0
-S-  Applied substitution rule convertipv4_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H31:  element(s, [begidx]) <= 255
<S>  New H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H8:  true
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H9:  true
-S-  Applied substitution rule convertipv4_rules(32).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New C1:  (element(s, [begidx]) - 48) mod 4294967296 mod 4294967296 >= 0
<S>  New C2:  (element(s, [begidx]) - 48) mod 4294967296 mod 4294967296 <= 
          4294967295
-S-  Applied substitution rule convertipv4_rules(34).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H2:  begidx >= 1
<S>  New H4:  endidx >= 1
<S>  New H1:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(35).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H3:  begidx <= 256
<S>  New H5:  endidx <= 256
<S>  New H1:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
***  Proved C1:  (element(s, [begidx]) - 48) mod 4294967296 mod 4294967296 >= 0
***  Proved C2:  (element(s, [begidx]) - 48) mod 4294967296 mod 4294967296 <= 
          4294967295
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_23.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H22).
***  Proved C3:  ctr + 1 >= rr_type__linelengthindex__first
     using hypothesis H31.
***  Proved C4:  ctr + 1 <= rr_type__linelengthindex__last
     using hypothesis H32.
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H19:  bytetotal >= 0
<S>  New H21:  (ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus 
          + (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) 
          mod unsigned_types__unsigned32__modulus >= 0
<S>  New C1:  (10 * ((ipv4_radix * bytetotal mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H20:  bytetotal <= 4294967295
<S>  New H22:  (ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus 
          + (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) 
          mod unsigned_types__unsigned32__modulus <= 4294967295
<S>  New C2:  (10 * ((ipv4_radix * bytetotal mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
>>>  Restructured hypothesis H41 into:
     >>>  H41:  endidx <= ctr + 1 or (req_num_separators < numseparators or (
          max_byte_value < (ipv4_radix * bytetotal mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or max_digits_per_byte < 
          numdigitsinbyte + 1))
-S-  Applied substitution rule convertipv4_rules(3).
     This was achieved by replacing all occurrences of req_num_separators by:
          3.
<S>  New H2:  numseparators <= 3
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (max_byte_value < (
          ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or max_digits_per_byte < 
          numdigitsinbyte + 1))
-S-  Applied substitution rule convertipv4_rules(4).
     This was achieved by replacing all occurrences of max_byte_value by:
          255.
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (255 < (ipv4_radix * 
          bytetotal mod unsigned_types__unsigned32__modulus + (element(s, [ctr])
           - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or max_digits_per_byte < 
          numdigitsinbyte + 1))
-S-  Applied substitution rule convertipv4_rules(5).
     This was achieved by replacing all occurrences of max_digits_per_byte by:
          3.
<S>  New H3:  numdigitsinbyte <= 3
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (255 < (ipv4_radix * 
          bytetotal mod unsigned_types__unsigned32__modulus + (element(s, [ctr])
           - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or numdigitsinbyte > 2))
-S-  Applied substitution rule convertipv4_rules(6).
     This was achieved by replacing all occurrences of ipv4_radix by:
          10.
<S>  New H21:  (10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H22:  (10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (255 < (10 * 
          bytetotal mod unsigned_types__unsigned32__modulus + (element(s, [ctr])
           - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or numdigitsinbyte > 2))
<S>  New C1:  (10 * ((10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C2:  (10 * ((10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
-S-  Applied substitution rule convertipv4_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= character__last)
<S>  New H11:  element(s, [ctr]) >= 0
<S>  New H47:  element(s, [ctr + 1]) >= 0
-S-  Applied substitution rule convertipv4_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  element(s, [ctr]) <= 255
<S>  New H48:  element(s, [ctr + 1]) <= 255
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H25:  numdigitsinbyte >= 0
<S>  New H27:  numdigitsinbyte >= - 1
<S>  New H35:  numseparators >= 0
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H26:  numdigitsinbyte <= 2147483647
<S>  New H28:  numdigitsinbyte <= 2147483646
<S>  New H36:  numseparators <= 2147483647
-S-  Applied substitution rule convertipv4_rules(32).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H21:  (10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 
          4294967296) mod 4294967296 >= 0
<S>  New H22:  (10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 
          4294967296) mod 4294967296 <= 4294967295
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (255 < (10 * 
          bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 4294967296) 
          mod 4294967296 or numdigitsinbyte > 2))
<S>  New C1:  (10 * ((10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) 
          mod 4294967296) mod 4294967296) mod 4294967296 + (element(s, [ctr + 1]
          ) - 48) mod 4294967296) mod 4294967296 >= 0
<S>  New C2:  (10 * ((10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) 
          mod 4294967296) mod 4294967296) mod 4294967296 + (element(s, [ctr + 1]
          ) - 48) mod 4294967296) mod 4294967296 <= 4294967295
-S-  Applied substitution rule convertipv4_rules(34).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H5:  begidx >= 1
<S>  New H7:  endidx >= 1
<S>  New H9:  ctr >= 1
<S>  New H31:  ctr >= 0
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(35).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H6:  begidx <= 256
<S>  New H8:  endidx <= 256
<S>  New H10:  ctr <= 256
<S>  New H32:  ctr <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
***  Proved C1:  (10 * ((10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 
          48) mod 4294967296) mod 4294967296) mod 4294967296 + (element(s, [ctr 
          + 1]) - 48) mod 4294967296) mod 4294967296 >= 0
***  Proved C2:  (10 * ((10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 
          48) mod 4294967296) mod 4294967296) mod 4294967296 + (element(s, [ctr 
          + 1]) - 48) mod 4294967296) mod 4294967296 <= 4294967295
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_24.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H34).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
***  Proved C3:  ctr + 1 >= rr_type__linelengthindex__first
     using hypothesis H39.
***  Proved C4:  ctr + 1 <= rr_type__linelengthindex__last
     using hypothesis H40.
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  bytetotal >= 0
<S>  New H29:  grandtotal >= 0
<S>  New H31:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H33:  true
<S>  New C1:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]
          ) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H28:  bytetotal <= 4294967295
<S>  New H30:  grandtotal <= 4294967295
<S>  New H32:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H34:  true
<S>  New C2:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]
          ) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
>>>  Restructured hypothesis H49 into:
     >>>  H49:  endidx <= ctr + 1 or (req_num_separators < numseparators + 1 or 
          (max_byte_value < 0 or max_digits_per_byte < 0))
-S-  Applied substitution rule convertipv4_rules(3).
     This was achieved by replacing all occurrences of req_num_separators by:
          3.
<S>  New H2:  numseparators <= 3
<S>  New H49:  endidx <= ctr + 1 or (numseparators > 2 or (max_byte_value < 0 
          or max_digits_per_byte < 0))
-S-  Applied substitution rule convertipv4_rules(4).
     This was achieved by replacing all occurrences of max_byte_value by:
          255.
<S>  New H31:  (256 mod unsigned_types__unsigned32__modulus * grandtotal mod 
          unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H32:  (256 mod unsigned_types__unsigned32__modulus * grandtotal mod 
          unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H49:  endidx <= ctr + 1 or (numseparators > 2 or max_digits_per_byte < 
          0)
-S-  Applied substitution rule convertipv4_rules(5).
     This was achieved by replacing all occurrences of max_digits_per_byte by:
          3.
<S>  New H3:  numdigitsinbyte <= 3
<S>  New H49:  endidx <= ctr + 1 or numseparators > 2
-S-  Applied substitution rule convertipv4_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= character__last)
<S>  New H11:  element(s, [ctr]) >= 0
<S>  New H55:  element(s, [ctr + 1]) >= 0
-S-  Applied substitution rule convertipv4_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  element(s, [ctr]) <= 255
<S>  New H56:  element(s, [ctr + 1]) <= 255
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H17:  numseparators >= 0
<S>  New H19:  numseparators >= - 1
<S>  New H35:  true
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H18:  numseparators <= 2147483647
<S>  New H20:  numseparators <= 2147483646
<S>  New H36:  true
-S-  Applied substitution rule convertipv4_rules(32).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H31:  (256 * grandtotal mod 4294967296 + bytetotal) mod 4294967296 >= 0
<S>  New H32:  (256 * grandtotal mod 4294967296 + bytetotal) mod 4294967296 <= 
          4294967295
<S>  New C1:  (element(s, [ctr + 1]) - 48) mod 4294967296 mod 4294967296 >= 0
<S>  New C2:  (element(s, [ctr + 1]) - 48) mod 4294967296 mod 4294967296 <= 
          4294967295
-S-  Applied substitution rule convertipv4_rules(34).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H5:  begidx >= 1
<S>  New H7:  endidx >= 1
<S>  New H9:  ctr >= 1
<S>  New H39:  ctr >= 0
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(35).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H6:  begidx <= 256
<S>  New H8:  endidx <= 256
<S>  New H10:  ctr <= 256
<S>  New H40:  ctr <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(39).
     This was achieved by replacing all occurrences of 
          separatorindextype__first by:
          1.
<S>  New H25:  numseparators >= 0
-S-  Applied substitution rule convertipv4_rules(40).
     This was achieved by replacing all occurrences of separatorindextype__last 
          by:
          4.
<S>  New H26:  numseparators <= 3
***  Proved C1:  (element(s, [ctr + 1]) - 48) mod 4294967296 mod 4294967296 >= 0
***  Proved C2:  (element(s, [ctr + 1]) - 48) mod 4294967296 mod 4294967296 <= 
          4294967295
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_25.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H36 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H11).
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [
          begidx]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [
          begidx]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
---  Hypothesis H42 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H45 has been replaced by "true".  (It is already present, as H9)
          .
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  1 >= natural__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  1 <= natural__last
***  Proved C1:  1 >= natural__first
     using hypothesis H8.
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H9:  true
<S>  New C2:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_26.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H28).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  numdigitsinbyte + 2 >= natural__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  numdigitsinbyte + 2 <= natural__last
***  Proved C1:  numdigitsinbyte + 2 >= natural__first
     using hypothesis H25.
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H26:  numdigitsinbyte <= 2147483647
<S>  New H28:  numdigitsinbyte <= 2147483646
<S>  New H36:  numseparators <= 2147483647
<S>  New C2:  numdigitsinbyte <= 2147483645
>>>  Restructured hypothesis H41 into:
     >>>  H41:  endidx <= ctr + 1 or (req_num_separators < numseparators or (
          max_byte_value < (ipv4_radix * bytetotal mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or max_digits_per_byte < 
          numdigitsinbyte + 1))
-S-  Applied substitution rule convertipv4_rules(3).
     This was achieved by replacing all occurrences of req_num_separators by:
          3.
<S>  New H2:  numseparators <= 3
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (max_byte_value < (
          ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or max_digits_per_byte < 
          numdigitsinbyte + 1))
-S-  Applied substitution rule convertipv4_rules(4).
     This was achieved by replacing all occurrences of max_byte_value by:
          255.
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (255 < (ipv4_radix * 
          bytetotal mod unsigned_types__unsigned32__modulus + (element(s, [ctr])
           - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or max_digits_per_byte < 
          numdigitsinbyte + 1))
-S-  Applied substitution rule convertipv4_rules(5).
     This was achieved by replacing all occurrences of max_digits_per_byte by:
          3.
<S>  New H3:  numdigitsinbyte <= 3
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (255 < (ipv4_radix * 
          bytetotal mod unsigned_types__unsigned32__modulus + (element(s, [ctr])
           - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or numdigitsinbyte > 2))
-S-  Applied substitution rule convertipv4_rules(6).
     This was achieved by replacing all occurrences of ipv4_radix by:
          10.
<S>  New H21:  (10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
<S>  New H22:  (10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
<S>  New H57:  (10 * ((10 * bytetotal mod unsigned_types__unsigned32__modulus + 
          (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
<S>  New H58:  (10 * ((10 * bytetotal mod unsigned_types__unsigned32__modulus + 
          (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (255 < (10 * 
          bytetotal mod unsigned_types__unsigned32__modulus + (element(s, [ctr])
           - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or numdigitsinbyte > 2))
-S-  Applied substitution rule convertipv4_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= character__last)
<S>  New H11:  element(s, [ctr]) >= 0
<S>  New H47:  element(s, [ctr + 1]) >= 0
-S-  Applied substitution rule convertipv4_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  element(s, [ctr]) <= 255
<S>  New H48:  element(s, [ctr + 1]) <= 255
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H25:  numdigitsinbyte >= 0
<S>  New H27:  numdigitsinbyte >= - 1
<S>  New H35:  numseparators >= 0
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H19:  bytetotal >= 0
<S>  New H21:  (10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H57:  (10 * ((10 * bytetotal mod unsigned_types__unsigned32__modulus + 
          (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H20:  bytetotal <= 4294967295
<S>  New H22:  (10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H58:  (10 * ((10 * bytetotal mod unsigned_types__unsigned32__modulus + 
          (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
-S-  Applied substitution rule convertipv4_rules(32).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (255 < (10 * 
          bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 4294967296) 
          mod 4294967296 or numdigitsinbyte > 2))
<S>  New H21:  (10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 
          4294967296) mod 4294967296 >= 0
<S>  New H57:  (10 * ((10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) 
          mod 4294967296) mod 4294967296) mod 4294967296 + (element(s, [ctr + 1]
          ) - 48) mod 4294967296) mod 4294967296 >= 0
<S>  New H22:  (10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 
          4294967296) mod 4294967296 <= 4294967295
<S>  New H58:  (10 * ((10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) 
          mod 4294967296) mod 4294967296) mod 4294967296 + (element(s, [ctr + 1]
          ) - 48) mod 4294967296) mod 4294967296 <= 4294967295
-S-  Applied substitution rule convertipv4_rules(34).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H5:  begidx >= 1
<S>  New H7:  endidx >= 1
<S>  New H9:  ctr >= 1
<S>  New H31:  ctr >= 0
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(35).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H6:  begidx <= 256
<S>  New H8:  endidx <= 256
<S>  New H10:  ctr <= 256
<S>  New H32:  ctr <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
***  Proved C2:  numdigitsinbyte <= 2147483645
     using hypothesis H3.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_27.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H34).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H66 on reading formula in, to give:
     %%%  H66:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  1 >= natural__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  1 <= natural__last
***  Proved C1:  1 >= natural__first
     using hypothesis H35.
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H18:  numseparators <= 2147483647
<S>  New H20:  numseparators <= 2147483646
<S>  New H36:  true
<S>  New C2:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_28.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H36 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H11).
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [
          begidx]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [
          begidx]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
---  Hypothesis H42 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H45 has been replaced by "true".  (It is already present, as H9)
          .
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  1 >= natural__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  1 <= natural__last
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H11).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  true
<S>  New H40:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [begidx]
          ) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C1:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  true
<S>  New H41:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [begidx]
          ) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New C2:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
>>>  Restructured hypothesis H24 into:
     >>>  H24:  endidx <= begidx or (req_num_separators < 0 or (max_byte_value 
          < 0 or max_digits_per_byte < 0))
-S-  Applied substitution rule convertipv4_rules(3).
     This was achieved by replacing all occurrences of req_num_separators by:
          3.
<S>  New H24:  endidx <= begidx or (max_byte_value < 0 or max_digits_per_byte < 
          0)
-S-  Applied substitution rule convertipv4_rules(4).
     This was achieved by replacing all occurrences of max_byte_value by:
          255.
<S>  New H24:  endidx <= begidx or max_digits_per_byte < 0
-S-  Applied substitution rule convertipv4_rules(5).
     This was achieved by replacing all occurrences of max_digits_per_byte by:
          3.
<S>  New H24:  endidx <= begidx
-S-  Applied substitution rule convertipv4_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= character__last)
<S>  New H30:  element(s, [begidx]) >= 0
-S-  Applied substitution rule convertipv4_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H31:  element(s, [begidx]) <= 255
<S>  New H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H8:  true
<S>  New H46:  true
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H9:  true
<S>  New H47:  true
-S-  Applied substitution rule convertipv4_rules(32).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H40:  (element(s, [begidx]) - 48) mod 4294967296 mod 4294967296 >= 0
<S>  New H41:  (element(s, [begidx]) - 48) mod 4294967296 mod 4294967296 <= 
          4294967295
<S>  New C1:  (element(s, [begidx]) - 48) mod 4294967296 mod 4294967296 mod 
          4294967296 >= 0
<S>  New C2:  (element(s, [begidx]) - 48) mod 4294967296 mod 4294967296 mod 
          4294967296 <= 4294967295
-S-  Applied substitution rule convertipv4_rules(34).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H2:  begidx >= 1
<S>  New H4:  endidx >= 1
<S>  New H1:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(35).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H3:  begidx <= 256
<S>  New H5:  endidx <= 256
<S>  New H1:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
***  Proved C1:  (element(s, [begidx]) - 48) mod 4294967296 mod 4294967296 mod 
          4294967296 >= 0
***  Proved C2:  (element(s, [begidx]) - 48) mod 4294967296 mod 4294967296 mod 
          4294967296 <= 4294967295
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_29.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H28).
%%%  Simplified H63 on reading formula in, to give:
     %%%  H63:  numdigitsinbyte + 2 >= natural__first
%%%  Simplified H64 on reading formula in, to give:
     %%%  H64:  numdigitsinbyte + 2 <= natural__last
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H58).
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H19:  bytetotal >= 0
<S>  New H21:  (ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus 
          + (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) 
          mod unsigned_types__unsigned32__modulus >= 0
<S>  New H57:  (10 * ((ipv4_radix * bytetotal mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H67:  grandtotal >= 0
<S>  New C1:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + (10 * ((
          ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H20:  bytetotal <= 4294967295
<S>  New H22:  (ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus 
          + (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) 
          mod unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H58:  (10 * ((ipv4_radix * bytetotal mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H68:  grandtotal <= 4294967295
<S>  New C2:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + (10 * ((
          ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
>>>  Restructured hypothesis H41 into:
     >>>  H41:  endidx <= ctr + 1 or (req_num_separators < numseparators or (
          max_byte_value < (ipv4_radix * bytetotal mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or max_digits_per_byte < 
          numdigitsinbyte + 1))
-S-  Applied substitution rule convertipv4_rules(3).
     This was achieved by replacing all occurrences of req_num_separators by:
          3.
<S>  New H2:  numseparators <= 3
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (max_byte_value < (
          ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or max_digits_per_byte < 
          numdigitsinbyte + 1))
-S-  Applied substitution rule convertipv4_rules(4).
     This was achieved by replacing all occurrences of max_byte_value by:
          255.
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (255 < (ipv4_radix * 
          bytetotal mod unsigned_types__unsigned32__modulus + (element(s, [ctr])
           - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or max_digits_per_byte < 
          numdigitsinbyte + 1))
<S>  New C1:  (256 mod unsigned_types__unsigned32__modulus * grandtotal mod 
          unsigned_types__unsigned32__modulus + (10 * ((ipv4_radix * bytetotal 
          mod unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C2:  (256 mod unsigned_types__unsigned32__modulus * grandtotal mod 
          unsigned_types__unsigned32__modulus + (10 * ((ipv4_radix * bytetotal 
          mod unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
-S-  Applied substitution rule convertipv4_rules(5).
     This was achieved by replacing all occurrences of max_digits_per_byte by:
          3.
<S>  New H3:  numdigitsinbyte <= 3
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (255 < (ipv4_radix * 
          bytetotal mod unsigned_types__unsigned32__modulus + (element(s, [ctr])
           - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or numdigitsinbyte > 2))
-S-  Applied substitution rule convertipv4_rules(6).
     This was achieved by replacing all occurrences of ipv4_radix by:
          10.
<S>  New H21:  (10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H22:  (10 * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H57:  (10 * ((10 * bytetotal mod unsigned_types__unsigned32__modulus + 
          (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H58:  (10 * ((10 * bytetotal mod unsigned_types__unsigned32__modulus + 
          (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (255 < (10 * 
          bytetotal mod unsigned_types__unsigned32__modulus + (element(s, [ctr])
           - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus or numdigitsinbyte > 2))
<S>  New C1:  (256 mod unsigned_types__unsigned32__modulus * grandtotal mod 
          unsigned_types__unsigned32__modulus + (10 * ((10 * bytetotal mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C2:  (256 mod unsigned_types__unsigned32__modulus * grandtotal mod 
          unsigned_types__unsigned32__modulus + (10 * ((10 * bytetotal mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
-S-  Applied substitution rule convertipv4_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= character__last)
<S>  New H11:  element(s, [ctr]) >= 0
<S>  New H47:  element(s, [ctr + 1]) >= 0
-S-  Applied substitution rule convertipv4_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  element(s, [ctr]) <= 255
<S>  New H48:  element(s, [ctr + 1]) <= 255
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H25:  numdigitsinbyte >= 0
<S>  New H27:  numdigitsinbyte >= - 1
<S>  New H35:  numseparators >= 0
<S>  New H63:  numdigitsinbyte >= - 2
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H26:  numdigitsinbyte <= 2147483647
<S>  New H28:  numdigitsinbyte <= 2147483646
<S>  New H36:  numseparators <= 2147483647
<S>  New H64:  numdigitsinbyte <= 2147483645
-S-  Applied substitution rule convertipv4_rules(32).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H21:  (10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 
          4294967296) mod 4294967296 >= 0
<S>  New H22:  (10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 
          4294967296) mod 4294967296 <= 4294967295
<S>  New H57:  (10 * ((10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) 
          mod 4294967296) mod 4294967296) mod 4294967296 + (element(s, [ctr + 1]
          ) - 48) mod 4294967296) mod 4294967296 >= 0
<S>  New H58:  (10 * ((10 * bytetotal mod 4294967296 + (element(s, [ctr]) - 48) 
          mod 4294967296) mod 4294967296) mod 4294967296 + (element(s, [ctr + 1]
          ) - 48) mod 4294967296) mod 4294967296 <= 4294967295
<S>  New H41:  endidx <= ctr + 1 or (3 < numseparators or (255 < (10 * 
          bytetotal mod 4294967296 + (element(s, [ctr]) - 48) mod 4294967296) 
          mod 4294967296 or numdigitsinbyte > 2))
<S>  New C1:  (256 * grandtotal mod 4294967296 + (10 * ((10 * bytetotal mod 
          4294967296 + (element(s, [ctr]) - 48) mod 4294967296) mod 4294967296) 
          mod 4294967296 + (element(s, [ctr + 1]) - 48) mod 4294967296) mod 
          4294967296) mod 4294967296 >= 0
<S>  New C2:  (256 * grandtotal mod 4294967296 + (10 * ((10 * bytetotal mod 
          4294967296 + (element(s, [ctr]) - 48) mod 4294967296) mod 4294967296) 
          mod 4294967296 + (element(s, [ctr + 1]) - 48) mod 4294967296) mod 
          4294967296) mod 4294967296 <= 4294967295
-S-  Applied substitution rule convertipv4_rules(34).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H5:  begidx >= 1
<S>  New H7:  endidx >= 1
<S>  New H9:  ctr >= 1
<S>  New H31:  ctr >= 0
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(35).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H6:  begidx <= 256
<S>  New H8:  endidx <= 256
<S>  New H10:  ctr <= 256
<S>  New H32:  ctr <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
***  Proved C1:  (256 * grandtotal mod 4294967296 + (10 * ((10 * bytetotal mod 
          4294967296 + (element(s, [ctr]) - 48) mod 4294967296) mod 4294967296) 
          mod 4294967296 + (element(s, [ctr + 1]) - 48) mod 4294967296) mod 
          4294967296) mod 4294967296 >= 0
***  Proved C2:  (256 * grandtotal mod 4294967296 + (10 * ((10 * bytetotal mod 
          4294967296 + (element(s, [ctr]) - 48) mod 4294967296) mod 4294967296) 
          mod 4294967296 + (element(s, [ctr + 1]) - 48) mod 4294967296) mod 
          4294967296) mod 4294967296 <= 4294967295
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_30.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H34).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H66 on reading formula in, to give:
     %%%  H66:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H71 on reading formula in, to give:
     %%%  H71:  1 >= natural__first
%%%  Simplified H72 on reading formula in, to give:
     %%%  H72:  1 <= natural__last
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H32).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * (
          ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * (
          ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  bytetotal >= 0
<S>  New H29:  grandtotal >= 0
<S>  New H31:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H33:  true
<S>  New H65:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C1:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * ((
          (max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H28:  bytetotal <= 4294967295
<S>  New H30:  grandtotal <= 4294967295
<S>  New H32:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H34:  true
<S>  New H66:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New C2:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * ((
          (max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
>>>  Restructured hypothesis H49 into:
     >>>  H49:  endidx <= ctr + 1 or (req_num_separators < numseparators + 1 or 
          (max_byte_value < 0 or max_digits_per_byte < 0))
-S-  Applied substitution rule convertipv4_rules(3).
     This was achieved by replacing all occurrences of req_num_separators by:
          3.
<S>  New H2:  numseparators <= 3
<S>  New H49:  endidx <= ctr + 1 or (numseparators > 2 or (max_byte_value < 0 
          or max_digits_per_byte < 0))
-S-  Applied substitution rule convertipv4_rules(4).
     This was achieved by replacing all occurrences of max_byte_value by:
          255.
<S>  New H31:  (256 mod unsigned_types__unsigned32__modulus * grandtotal mod 
          unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H32:  (256 mod unsigned_types__unsigned32__modulus * grandtotal mod 
          unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H49:  endidx <= ctr + 1 or (numseparators > 2 or max_digits_per_byte < 
          0)
<S>  New C1:  (256 mod unsigned_types__unsigned32__modulus * ((256 mod 
          unsigned_types__unsigned32__modulus * grandtotal mod 
          unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C2:  (256 mod unsigned_types__unsigned32__modulus * ((256 mod 
          unsigned_types__unsigned32__modulus * grandtotal mod 
          unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
-S-  Applied substitution rule convertipv4_rules(5).
     This was achieved by replacing all occurrences of max_digits_per_byte by:
          3.
<S>  New H3:  numdigitsinbyte <= 3
<S>  New H49:  endidx <= ctr + 1 or numseparators > 2
-S-  Applied substitution rule convertipv4_rules(13).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= character__last)
<S>  New H11:  element(s, [ctr]) >= 0
<S>  New H55:  element(s, [ctr + 1]) >= 0
-S-  Applied substitution rule convertipv4_rules(14).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H12:  element(s, [ctr]) <= 255
<S>  New H56:  element(s, [ctr + 1]) <= 255
<S>  New H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [i___1]
          ) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H17:  numseparators >= 0
<S>  New H19:  numseparators >= - 1
<S>  New H35:  true
<S>  New H71:  true
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H18:  numseparators <= 2147483647
<S>  New H20:  numseparators <= 2147483646
<S>  New H36:  true
<S>  New H72:  true
-S-  Applied substitution rule convertipv4_rules(32).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H65:  (element(s, [ctr + 1]) - 48) mod 4294967296 mod 4294967296 >= 0
<S>  New H66:  (element(s, [ctr + 1]) - 48) mod 4294967296 mod 4294967296 <= 
          4294967295
<S>  New H31:  (256 * grandtotal mod 4294967296 + bytetotal) mod 4294967296 >= 0
<S>  New H32:  (256 * grandtotal mod 4294967296 + bytetotal) mod 4294967296 <= 
          4294967295
<S>  New C1:  (256 * ((256 * grandtotal mod 4294967296 + bytetotal) mod 
          4294967296) mod 4294967296 + (element(s, [ctr + 1]) - 48) mod 
          4294967296 mod 4294967296) mod 4294967296 >= 0
<S>  New C2:  (256 * ((256 * grandtotal mod 4294967296 + bytetotal) mod 
          4294967296) mod 4294967296 + (element(s, [ctr + 1]) - 48) mod 
          4294967296 mod 4294967296) mod 4294967296 <= 4294967295
-S-  Applied substitution rule convertipv4_rules(34).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H5:  begidx >= 1
<S>  New H7:  endidx >= 1
<S>  New H9:  ctr >= 1
<S>  New H39:  ctr >= 0
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(35).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H6:  begidx <= 256
<S>  New H8:  endidx <= 256
<S>  New H10:  ctr <= 256
<S>  New H40:  ctr <= 255
<S>  New H4:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule convertipv4_rules(39).
     This was achieved by replacing all occurrences of 
          separatorindextype__first by:
          1.
<S>  New H25:  numseparators >= 0
-S-  Applied substitution rule convertipv4_rules(40).
     This was achieved by replacing all occurrences of separatorindextype__last 
          by:
          4.
<S>  New H26:  numseparators <= 3
***  Proved C1:  (256 * ((256 * grandtotal mod 4294967296 + bytetotal) mod 
          4294967296) mod 4294967296 + (element(s, [ctr + 1]) - 48) mod 
          4294967296 mod 4294967296) mod 4294967296 >= 0
***  Proved C2:  (256 * ((256 * grandtotal mod 4294967296 + bytetotal) mod 
          4294967296) mod 4294967296 + (element(s, [ctr + 1]) - 48) mod 
          4294967296 mod 4294967296) mod 4294967296 <= 4294967295
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_31.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
-S-  Applied substitution rule convertipv4_rules(2).
     This was achieved by replacing all occurrences of num_bytes by:
          4.
<S>  New C1:  4 >= natural__first
<S>  New C2:  4 <= natural__last
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H8:  true
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H9:  true
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_32.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
-S-  Applied substitution rule convertipv4_rules(2).
     This was achieved by replacing all occurrences of num_bytes by:
          4.
<S>  New C1:  4 >= natural__first
<S>  New C2:  4 <= natural__last
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H25:  numdigitsinbyte >= 0
<S>  New H27:  numdigitsinbyte >= - 1
<S>  New H35:  numseparators >= 0
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H26:  numdigitsinbyte <= 2147483647
<S>  New H28:  numdigitsinbyte <= 2147483646
<S>  New H36:  numseparators <= 2147483647
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_33.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
-S-  Applied substitution rule convertipv4_rules(2).
     This was achieved by replacing all occurrences of num_bytes by:
          4.
<S>  New C1:  4 >= natural__first
<S>  New C2:  4 <= natural__last
-S-  Applied substitution rule convertipv4_rules(18).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H17:  numseparators >= 0
<S>  New H19:  numseparators >= - 1
<S>  New H35:  true
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(19).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H18:  numseparators <= 2147483647
<S>  New H20:  numseparators <= 2147483646
<S>  New H36:  true
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_34.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H36 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H11).
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [
          begidx]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [
          begidx]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
---  Hypothesis H42 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H45 has been replaced by "true".  (It is already present, as H9)
          .
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  1 >= natural__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  1 <= natural__last
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H11).
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
%%%  Simplified H54 on reading formula in, to give:
     %%%  H54:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= 1 and 1 <= rr_type__linelengthindex__last)
---  Hypothesis H56 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H57 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H46).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H47).
%%%  Simplified H64 on reading formula in, to give:
     %%%  H64:  1 <= max_digits_per_byte
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [
          begidx]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= max_byte_value
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H53).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
***  Proved C1:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
     using hypothesis H52.
***  Proved C2:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
     using hypothesis H53.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_35.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified H38 on reading formula in, to give:
     %%%  H38:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= 1 and 1 <= rr_type__linelengthindex__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H45 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H11).
***  Proved C1:  0 >= unsigned_types__unsigned32__first
     using hypothesis H10.
***  Proved C2:  0 <= unsigned_types__unsigned32__last
     using hypothesis H11.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_36.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= 1 and 1 <= rr_type__linelengthindex__last)
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H35 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H11).
***  Proved C1:  0 >= unsigned_types__unsigned32__first
     using hypothesis H10.
***  Proved C2:  0 <= unsigned_types__unsigned32__last
     using hypothesis H11.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_37.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H28).
%%%  Simplified H63 on reading formula in, to give:
     %%%  H63:  numdigitsinbyte + 2 >= natural__first
%%%  Simplified H64 on reading formula in, to give:
     %%%  H64:  numdigitsinbyte + 2 <= natural__last
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H58).
%%%  Simplified H71 on reading formula in, to give:
     %%%  H71:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(separatorindexarray, [i___1]) and element(
          separatorindexarray, [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H63).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H64).
%%%  Simplified H81 on reading formula in, to give:
     %%%  H81:  numdigitsinbyte + 2 <= max_digits_per_byte
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H70).
***  Proved C1:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * grandtotal mod unsigned_types__unsigned32__modulus + (10 * ((
          ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
     using hypothesis H69.
***  Proved C2:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * grandtotal mod unsigned_types__unsigned32__modulus + (10 * ((
          ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
     using hypothesis H70.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_38.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H34).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H66 on reading formula in, to give:
     %%%  H66:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H71 on reading formula in, to give:
     %%%  H71:  1 >= natural__first
%%%  Simplified H72 on reading formula in, to give:
     %%%  H72:  1 <= natural__last
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H32).
%%%  Simplified H77 on reading formula in, to give:
     %%%  H77:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          (((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          (((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(update(separatorindexarray, [numseparators + 1], ctr), [
          i___1]) and element(update(separatorindexarray, [numseparators + 1], 
          ctr), [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H71).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H72).
%%%  Simplified H89 on reading formula in, to give:
     %%%  H89:  1 <= max_digits_per_byte
%%%  Simplified H90 on reading formula in, to give:
     %%%  H90:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= max_byte_value
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H78).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * (
          ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * (
          ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
***  Proved C1:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * (((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
     using hypothesis H77.
***  Proved C2:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * (((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
     using hypothesis H78.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_39.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(separatorindexarray, [i___1]) and element(
          separatorindexarray, [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H28).
***  Proved C1:  grandtotal >= unsigned_types__unsigned32__first
     using hypothesis H67.
***  Proved C2:  grandtotal <= unsigned_types__unsigned32__last
     using hypothesis H68.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_40.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
%%%  Simplified H63 on reading formula in, to give:
     %%%  H63:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(update(separatorindexarray, [numseparators + 1], ctr), [
          i___1]) and element(update(separatorindexarray, [numseparators + 1], 
          ctr), [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H62).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H32).
***  Proved C1:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
     using hypothesis H31.
***  Proved C2:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
     using hypothesis H32.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_41.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
%%%  Simplified H45 on reading formula in, to give:
     %%%  H45:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(separatorindexarray, [i___1]) and element(
          separatorindexarray, [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H28).
***  Proved C1:  grandtotal >= unsigned_types__unsigned32__first
     using hypothesis H57.
***  Proved C2:  grandtotal <= unsigned_types__unsigned32__last
     using hypothesis H58.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_42.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(update(separatorindexarray, [numseparators + 1], ctr), [
          i___1]) and element(update(separatorindexarray, [numseparators + 1], 
          ctr), [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H32).
***  Proved C1:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
     using hypothesis H31.
***  Proved C2:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
     using hypothesis H32.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_43.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H36 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H11).
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [
          begidx]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [
          begidx]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
---  Hypothesis H42 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H45 has been replaced by "true".  (It is already present, as H9)
          .
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  1 >= natural__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  1 <= natural__last
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H11).
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
%%%  Simplified H54 on reading formula in, to give:
     %%%  H54:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= 1 and 1 <= rr_type__linelengthindex__last)
---  Hypothesis H56 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H57 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H46).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H47).
%%%  Simplified H62 on reading formula in, to give:
     %%%  H62:  not (separatorsok(s, mk__separatorindexarraytype(1)) and (0 = 
          req_num_separators and 1 <= max_digits_per_byte and (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= max_byte_value))
-S-  Applied substitution rule convertipv4_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__a_record_type__invalid_ipv4_addr by:
          0.
<S>  New C1:  0 >= unsigned_types__unsigned32__first
<S>  New C2:  0 <= unsigned_types__unsigned32__last
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  true
<S>  New H40:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [begidx]
          ) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H52:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  true
<S>  New H41:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [begidx]
          ) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H53:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_44.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified H38 on reading formula in, to give:
     %%%  H38:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= 1 and 1 <= rr_type__linelengthindex__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H45 has been replaced by "true".  (It is already present, as H9)
          .
-S-  Applied substitution rule convertipv4_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__a_record_type__invalid_ipv4_addr by:
          0.
<S>  New C1:  0 >= unsigned_types__unsigned32__first
<S>  New C2:  0 <= unsigned_types__unsigned32__last
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  true
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  true
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_45.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= 1 and 1 <= rr_type__linelengthindex__last)
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H35 has been replaced by "true".  (It is already present, as H9)
          .
-S-  Applied substitution rule convertipv4_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__a_record_type__invalid_ipv4_addr by:
          0.
<S>  New C1:  0 >= unsigned_types__unsigned32__first
<S>  New C2:  0 <= unsigned_types__unsigned32__last
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  true
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  true
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_46.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H28).
%%%  Simplified H63 on reading formula in, to give:
     %%%  H63:  numdigitsinbyte + 2 >= natural__first
%%%  Simplified H64 on reading formula in, to give:
     %%%  H64:  numdigitsinbyte + 2 <= natural__last
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H58).
%%%  Simplified H71 on reading formula in, to give:
     %%%  H71:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(separatorindexarray, [i___1]) and element(
          separatorindexarray, [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H63).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H64).
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  not (separatorsok(s, separatorindexarray) and (numseparators = 
          req_num_separators and numdigitsinbyte + 2 <= max_digits_per_byte and 
          (10 * ((ipv4_radix * bytetotal mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= max_byte_value))
-S-  Applied substitution rule convertipv4_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__a_record_type__invalid_ipv4_addr by:
          0.
<S>  New C1:  0 >= unsigned_types__unsigned32__first
<S>  New C2:  0 <= unsigned_types__unsigned32__last
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H19:  bytetotal >= 0
<S>  New H21:  (ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus 
          + (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) 
          mod unsigned_types__unsigned32__modulus >= 0
<S>  New H57:  (10 * ((ipv4_radix * bytetotal mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H67:  grandtotal >= 0
<S>  New H69:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + (10 * ((
          ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H20:  bytetotal <= 4294967295
<S>  New H22:  (ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus 
          + (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) 
          mod unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H58:  (10 * ((ipv4_radix * bytetotal mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H68:  grandtotal <= 4294967295
<S>  New H70:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + (10 * ((
          ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_47.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H34).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H66 on reading formula in, to give:
     %%%  H66:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H71 on reading formula in, to give:
     %%%  H71:  1 >= natural__first
%%%  Simplified H72 on reading formula in, to give:
     %%%  H72:  1 <= natural__last
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H32).
%%%  Simplified H77 on reading formula in, to give:
     %%%  H77:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          (((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          (((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(update(separatorindexarray, [numseparators + 1], ctr), [
          i___1]) and element(update(separatorindexarray, [numseparators + 1], 
          ctr), [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H71).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H72).
%%%  Simplified H87 on reading formula in, to give:
     %%%  H87:  not (separatorsok(s, update(separatorindexarray, [numseparators 
          + 1], ctr)) and (numseparators + 1 = req_num_separators and 1 <= 
          max_digits_per_byte and (0 mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr + 1]) - 48) mod unsigned_types__unsigned32__modulus) 
          mod unsigned_types__unsigned32__modulus <= max_byte_value))
-S-  Applied substitution rule convertipv4_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__a_record_type__invalid_ipv4_addr by:
          0.
<S>  New C1:  0 >= unsigned_types__unsigned32__first
<S>  New C2:  0 <= unsigned_types__unsigned32__last
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  bytetotal >= 0
<S>  New H29:  grandtotal >= 0
<S>  New H31:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H33:  true
<S>  New H65:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H77:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * (
          ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H28:  bytetotal <= 4294967295
<S>  New H30:  grandtotal <= 4294967295
<S>  New H32:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H34:  true
<S>  New H66:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H78:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * (
          ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_48.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(separatorindexarray, [i___1]) and element(
          separatorindexarray, [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H28).
-S-  Applied substitution rule convertipv4_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__a_record_type__invalid_ipv4_addr by:
          0.
<S>  New C1:  0 >= unsigned_types__unsigned32__first
<S>  New C2:  0 <= unsigned_types__unsigned32__last
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H19:  bytetotal >= 0
<S>  New H21:  (ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus 
          + (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) 
          mod unsigned_types__unsigned32__modulus >= 0
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H20:  bytetotal <= 4294967295
<S>  New H22:  (ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus 
          + (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) 
          mod unsigned_types__unsigned32__modulus <= 4294967295
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_49.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
%%%  Simplified H63 on reading formula in, to give:
     %%%  H63:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(update(separatorindexarray, [numseparators + 1], ctr), [
          i___1]) and element(update(separatorindexarray, [numseparators + 1], 
          ctr), [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H62).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H36).
-S-  Applied substitution rule convertipv4_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__a_record_type__invalid_ipv4_addr by:
          0.
<S>  New C1:  0 >= unsigned_types__unsigned32__first
<S>  New C2:  0 <= unsigned_types__unsigned32__last
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  bytetotal >= 0
<S>  New H29:  grandtotal >= 0
<S>  New H31:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H33:  true
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H28:  bytetotal <= 4294967295
<S>  New H30:  grandtotal <= 4294967295
<S>  New H32:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H34:  true
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_50.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
%%%  Simplified H45 on reading formula in, to give:
     %%%  H45:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(separatorindexarray, [i___1]) and element(
          separatorindexarray, [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H28).
-S-  Applied substitution rule convertipv4_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__a_record_type__invalid_ipv4_addr by:
          0.
<S>  New C1:  0 >= unsigned_types__unsigned32__first
<S>  New C2:  0 <= unsigned_types__unsigned32__last
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H19:  bytetotal >= 0
<S>  New H21:  (ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus 
          + (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) 
          mod unsigned_types__unsigned32__modulus >= 0
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H20:  bytetotal <= 4294967295
<S>  New H22:  (ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus 
          + (element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) 
          mod unsigned_types__unsigned32__modulus <= 4294967295
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_51.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(update(separatorindexarray, [numseparators + 1], ctr), [
          i___1]) and element(update(separatorindexarray, [numseparators + 1], 
          ctr), [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H36).
-S-  Applied substitution rule convertipv4_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__a_record_type__invalid_ipv4_addr by:
          0.
<S>  New C1:  0 >= unsigned_types__unsigned32__first
<S>  New C2:  0 <= unsigned_types__unsigned32__last
-S-  Applied substitution rule convertipv4_rules(28).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H27:  bytetotal >= 0
<S>  New H29:  grandtotal >= 0
<S>  New H31:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H33:  true
<S>  New C1:  true
-S-  Applied substitution rule convertipv4_rules(29).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H28:  bytetotal <= 4294967295
<S>  New H30:  grandtotal <= 4294967295
<S>  New H32:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus <= 4294967295
<S>  New H34:  true
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_52.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H36 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H11).
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [
          begidx]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [
          begidx]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
---  Hypothesis H42 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H45 has been replaced by "true".  (It is already present, as H9)
          .
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  1 >= natural__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  1 <= natural__last
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H11).
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
%%%  Simplified H54 on reading formula in, to give:
     %%%  H54:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= 1 and 1 <= rr_type__linelengthindex__last)
---  Hypothesis H56 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H57 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H46).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H47).
%%%  Simplified H64 on reading formula in, to give:
     %%%  H64:  1 <= max_digits_per_byte
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [
          begidx]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= max_byte_value
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H53).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
***  Proved C1:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
     using hypothesis H52.
***  Proved C2:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
     using hypothesis H53.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_53.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified H38 on reading formula in, to give:
     %%%  H38:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= 1 and 1 <= rr_type__linelengthindex__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H45 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H11).
***  Proved C1:  0 >= unsigned_types__unsigned32__first
     using hypothesis H10.
***  Proved C2:  0 <= unsigned_types__unsigned32__last
     using hypothesis H11.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_54.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= 1 and 1 <= rr_type__linelengthindex__last)
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H35 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H11).
***  Proved C1:  0 >= unsigned_types__unsigned32__first
     using hypothesis H10.
***  Proved C2:  0 <= unsigned_types__unsigned32__last
     using hypothesis H11.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_55.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H36 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H11).
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [
          begidx]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [
          begidx]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
---  Hypothesis H42 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H45 has been replaced by "true".  (It is already present, as H9)
          .
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  1 >= natural__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  1 <= natural__last
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H11).
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  (0 mod unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
%%%  Simplified H54 on reading formula in, to give:
     %%%  H54:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= 1 and 1 <= rr_type__linelengthindex__last)
---  Hypothesis H56 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H57 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H46).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H47).
%%%  Simplified H62 on reading formula in, to give:
     %%%  H62:  not (separatorsok(s, mk__separatorindexarraytype(1)) and (0 = 
          req_num_separators and 1 <= max_digits_per_byte and (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [begidx]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= max_byte_value))
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H63).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H64).
***  Proved C1:  rr_type__a_record_type__invalid_ipv4_addr >= 
          unsigned_types__unsigned32__first
     using hypothesis H63.
***  Proved C2:  rr_type__a_record_type__invalid_ipv4_addr <= 
          unsigned_types__unsigned32__last
     using hypothesis H64.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_56.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified H38 on reading formula in, to give:
     %%%  H38:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= 1 and 1 <= rr_type__linelengthindex__last)
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H45 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H47).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H48).
***  Proved C1:  rr_type__a_record_type__invalid_ipv4_addr >= 
          unsigned_types__unsigned32__first
     using hypothesis H47.
***  Proved C2:  rr_type__a_record_type__invalid_ipv4_addr <= 
          unsigned_types__unsigned32__last
     using hypothesis H48.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_57.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H6 has been replaced by "true".  (It is already present, as H2).
---  Hypothesis H7 has been replaced by "true".  (It is already present, as H3).
---  Hypothesis H12 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H15 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H16 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H25 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H26 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= 1 and 1 <= rr_type__linelengthindex__last)
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H31 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H11).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H35 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H38).
***  Proved C1:  rr_type__a_record_type__invalid_ipv4_addr >= 
          unsigned_types__unsigned32__first
     using hypothesis H37.
***  Proved C2:  rr_type__a_record_type__invalid_ipv4_addr <= 
          unsigned_types__unsigned32__last
     using hypothesis H38.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_58.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H28).
%%%  Simplified H63 on reading formula in, to give:
     %%%  H63:  numdigitsinbyte + 2 >= natural__first
%%%  Simplified H64 on reading formula in, to give:
     %%%  H64:  numdigitsinbyte + 2 <= natural__last
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H58).
%%%  Simplified H71 on reading formula in, to give:
     %%%  H71:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(separatorindexarray, [i___1]) and element(
          separatorindexarray, [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H63).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H64).
%%%  Simplified H81 on reading formula in, to give:
     %%%  H81:  numdigitsinbyte + 2 <= max_digits_per_byte
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H69).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H70).
***  Proved C1:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * grandtotal mod unsigned_types__unsigned32__modulus + (10 * ((
          ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
     using hypothesis H69.
***  Proved C2:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * grandtotal mod unsigned_types__unsigned32__modulus + (10 * ((
          ipv4_radix * bytetotal mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
     using hypothesis H70.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_59.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H34).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H66 on reading formula in, to give:
     %%%  H66:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H71 on reading formula in, to give:
     %%%  H71:  1 >= natural__first
%%%  Simplified H72 on reading formula in, to give:
     %%%  H72:  1 <= natural__last
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H32).
%%%  Simplified H77 on reading formula in, to give:
     %%%  H77:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          (((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          (((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(update(separatorindexarray, [numseparators + 1], ctr), [
          i___1]) and element(update(separatorindexarray, [numseparators + 1], 
          ctr), [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H71).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H72).
%%%  Simplified H89 on reading formula in, to give:
     %%%  H89:  1 <= max_digits_per_byte
%%%  Simplified H90 on reading formula in, to give:
     %%%  H90:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= max_byte_value
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H78).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H94 has been replaced by "true".  (It is already present, as 
          H78).
---  Hypothesis H95 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H96 has been replaced by "true".  (It is already present, as 
          H78).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * (
          ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * (
          ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
***  Proved C1:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * (((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
     using hypothesis H77.
***  Proved C2:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * (((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
     using hypothesis H78.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_60.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(separatorindexarray, [i___1]) and element(
          separatorindexarray, [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H68).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H68).
***  Proved C1:  grandtotal >= unsigned_types__unsigned32__first
     using hypothesis H67.
***  Proved C2:  grandtotal <= unsigned_types__unsigned32__last
     using hypothesis H68.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_61.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
%%%  Simplified H63 on reading formula in, to give:
     %%%  H63:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(update(separatorindexarray, [numseparators + 1], ctr), [
          i___1]) and element(update(separatorindexarray, [numseparators + 1], 
          ctr), [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H62).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H32).
***  Proved C1:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
     using hypothesis H31.
***  Proved C2:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
     using hypothesis H32.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_62.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
%%%  Simplified H45 on reading formula in, to give:
     %%%  H45:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(separatorindexarray, [i___1]) and element(
          separatorindexarray, [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H58).
***  Proved C1:  grandtotal >= unsigned_types__unsigned32__first
     using hypothesis H57.
***  Proved C2:  grandtotal <= unsigned_types__unsigned32__last
     using hypothesis H58.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_63.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(update(separatorindexarray, [numseparators + 1], ctr), [
          i___1]) and element(update(separatorindexarray, [numseparators + 1], 
          ctr), [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H32).
***  Proved C1:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
     using hypothesis H31.
***  Proved C2:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus 
          * grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
     using hypothesis H32.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_64.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H28).
%%%  Simplified H63 on reading formula in, to give:
     %%%  H63:  numdigitsinbyte + 2 >= natural__first
%%%  Simplified H64 on reading formula in, to give:
     %%%  H64:  numdigitsinbyte + 2 <= natural__last
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H58).
%%%  Simplified H71 on reading formula in, to give:
     %%%  H71:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(separatorindexarray, [i___1]) and element(
          separatorindexarray, [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H63).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H64).
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  not (separatorsok(s, separatorindexarray) and (numseparators = 
          req_num_separators and numdigitsinbyte + 2 <= max_digits_per_byte and 
          (10 * ((ipv4_radix * bytetotal mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr]) - 48) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= max_byte_value))
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H80).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H81).
***  Proved C1:  rr_type__a_record_type__invalid_ipv4_addr >= 
          unsigned_types__unsigned32__first
     using hypothesis H80.
***  Proved C2:  rr_type__a_record_type__invalid_ipv4_addr <= 
          unsigned_types__unsigned32__last
     using hypothesis H81.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_65.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H34).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H66 on reading formula in, to give:
     %%%  H66:  (0 mod unsigned_types__unsigned32__modulus + (element(s, [ctr + 
          1]) - 48) mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified H71 on reading formula in, to give:
     %%%  H71:  1 >= natural__first
%%%  Simplified H72 on reading formula in, to give:
     %%%  H72:  1 <= natural__last
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H32).
%%%  Simplified H77 on reading formula in, to give:
     %%%  H77:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          (((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned32__first
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  ((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          (((max_byte_value + 1) mod unsigned_types__unsigned32__modulus * 
          grandtotal mod unsigned_types__unsigned32__modulus + bytetotal) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus + (0 mod 
          unsigned_types__unsigned32__modulus + (element(s, [ctr + 1]) - 48) 
          mod unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus) mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned32__last
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(update(separatorindexarray, [numseparators + 1], ctr), [
          i___1]) and element(update(separatorindexarray, [numseparators + 1], 
          ctr), [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H71).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H72).
%%%  Simplified H87 on reading formula in, to give:
     %%%  H87:  not (separatorsok(s, update(separatorindexarray, [numseparators 
          + 1], ctr)) and (numseparators + 1 = req_num_separators and 1 <= 
          max_digits_per_byte and (0 mod unsigned_types__unsigned32__modulus + (
          element(s, [ctr + 1]) - 48) mod unsigned_types__unsigned32__modulus) 
          mod unsigned_types__unsigned32__modulus <= max_byte_value))
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H89).
***  Proved C1:  rr_type__a_record_type__invalid_ipv4_addr >= 
          unsigned_types__unsigned32__first
     using hypothesis H88.
***  Proved C2:  rr_type__a_record_type__invalid_ipv4_addr <= 
          unsigned_types__unsigned32__last
     using hypothesis H89.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_66.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(separatorindexarray, [i___1]) and element(
          separatorindexarray, [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H64).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H65).
***  Proved C1:  rr_type__a_record_type__invalid_ipv4_addr >= 
          unsigned_types__unsigned32__first
     using hypothesis H64.
***  Proved C2:  rr_type__a_record_type__invalid_ipv4_addr <= 
          unsigned_types__unsigned32__last
     using hypothesis H65.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_67.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H40).
%%%  Simplified H63 on reading formula in, to give:
     %%%  H63:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(update(separatorindexarray, [numseparators + 1], ctr), [
          i___1]) and element(update(separatorindexarray, [numseparators + 1], 
          ctr), [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H62).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H72).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H73).
***  Proved C1:  rr_type__a_record_type__invalid_ipv4_addr >= 
          unsigned_types__unsigned32__first
     using hypothesis H72.
***  Proved C2:  rr_type__a_record_type__invalid_ipv4_addr <= 
          unsigned_types__unsigned32__last
     using hypothesis H73.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_68.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H17 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H32).
%%%  Simplified H45 on reading formula in, to give:
     %%%  H45:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(separatorindexarray, [i___1]) and element(
          separatorindexarray, [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
***  Proved C1:  rr_type__a_record_type__invalid_ipv4_addr >= 
          unsigned_types__unsigned32__first
     using hypothesis H54.
***  Proved C2:  rr_type__a_record_type__invalid_ipv4_addr <= 
          unsigned_types__unsigned32__last
     using hypothesis H55.
***  PROVED VC.


@@@@@@@@@@  VC: function_convertipv4_69.  @@@@@@@@@@
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H13 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H14 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H24 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H10).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  for_all(i___1 : integer, separatorindextype__first <= i___1 and 
          i___1 <= separatorindextype__last -> rr_type__linelengthindex__first 
          <= element(update(separatorindexarray, [numseparators + 1], ctr), [
          i___1]) and element(update(separatorindexarray, [numseparators + 1], 
          ctr), [i___1]) <= rr_type__linelengthindex__last)
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H20).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H62).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H63).
***  Proved C1:  rr_type__a_record_type__invalid_ipv4_addr >= 
          unsigned_types__unsigned32__first
     using hypothesis H62.
***  Proved C2:  rr_type__a_record_type__invalid_ipv4_addr <= 
          unsigned_types__unsigned32__last
     using hypothesis H63.
***  PROVED VC.

