*****************************************************************************
                       Semantic Analysis of SPARK Text
                             Examiner GPL Edition

*****************************************************************************



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

procedure Parser_Utilities.convert8BitUnsigned






@@@@@@@@@@  VC: procedure_convert8bitunsigned_1.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
-S-  Applied substitution rule convert8bitu_rules(13).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New C1:  true
-S-  Applied substitution rule convert8bitu_rules(14).
     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: procedure_convert8bitunsigned_2.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
-S-  Applied substitution rule convert8bitu_rules(23).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New C1:  true
-S-  Applied substitution rule convert8bitu_rules(24).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_3.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
-S-  Applied substitution rule convert8bitu_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New C1:  endidx >= - 2147483648
<S>  New C3:  begidx >= - 2147483648
-S-  Applied substitution rule convert8bitu_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New C2:  endidx <= 2147483647
<S>  New C4:  begidx <= 2147483647
-S-  Applied substitution rule convert8bitu_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H2:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(
          zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 
          character__last)
-S-  Applied substitution rule convert8bitu_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H2:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(
          zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 255)
-S-  Applied substitution rule convert8bitu_rules(13).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H7:  true
-S-  Applied substitution rule convert8bitu_rules(14).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H8:  true
-S-  Applied substitution rule convert8bitu_rules(23).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H9:  true
-S-  Applied substitution rule convert8bitu_rules(24).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H10:  true
-S-  Applied substitution rule convert8bitu_rules(29).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H3:  begidx >= 1
<S>  New H5:  endidx >= 1
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(zonefileline, [i___1]) 
          and element(zonefileline, [i___1]) <= 255)
-S-  Applied substitution rule convert8bitu_rules(30).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H4:  begidx <= 256
<S>  New H6:  endidx <= 256
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 
          255)
***  Proved C1:  endidx >= - 2147483648
     using hypothesis H5.
***  Proved C3:  begidx >= - 2147483648
     using hypothesis H3.
***  Proved C2:  endidx <= 2147483647
     using hypothesis H6.
***  Proved C4:  begidx <= 2147483647
     using hypothesis H4.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_4.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
***  Proved C1:  begidx <= endidx -> endidx >= integer__first and endidx <= 
          integer__last
     using hypotheses H11 & H12.
***  Proved C2:  begidx <= endidx -> begidx >= integer__first and begidx <= 
          integer__last
     using hypotheses H13 & H14.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_5.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
%%%  Simplified C8 on reading formula in, to give:
     %%%  C8:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
%%%  Simplified C11 on reading formula in, to give:
     %%%  C11:  true
***  Proved C3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
     using hypothesis H2.
***  Proved C4:  begidx >= rr_type__linelengthindex__first
     using hypothesis H3.
***  Proved C5:  begidx <= rr_type__linelengthindex__last
     using hypothesis H4.
***  Proved C6:  endidx >= rr_type__linelengthindex__first
     using hypothesis H5.
***  Proved C7:  endidx <= rr_type__linelengthindex__last
     using hypothesis H6.
***  Proved C8:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
     using hypothesis H1.
***  Proved C9:  begidx >= integer__first
     using hypothesis H13.
***  Proved C10:  begidx <= integer__last
     using hypothesis H14.
***  Proved C11:  true
***  Proved C12:  begidx <= endidx
     using hypothesis H17.
-S-  Applied substitution rule convert8bitu_rules(1).
     This was achieved by replacing all occurrences of 
          unsigned_types__max_8bit_val by:
          255.
<S>  New C2:  true
***  Proved C2:  true
+++  Using "A->B, A |- B" on hypotheses H15 & H17 yields a new hypothesis:
     +++  H18:  endidx >= integer__first and endidx <= integer__last
+++  Using "A->B, A |- B" on hypotheses H16 & H17 yields a new hypothesis:
     +++  H19:  begidx >= integer__first and begidx <= integer__last
-S-  Applied substitution rule convert8bitu_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H11:  endidx >= - 2147483648
<S>  New H13:  begidx >= - 2147483648
<S>  New H15:  begidx <= endidx -> endidx >= - 2147483648 and endidx <= 
          integer__last
<S>  New H16:  begidx <= endidx -> begidx >= - 2147483648 and begidx <= 
          integer__last
<S>  New H18:  endidx >= - 2147483648 and endidx <= integer__last
<S>  New H19:  begidx >= - 2147483648 and begidx <= integer__last
-S-  Applied substitution rule convert8bitu_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H12:  endidx <= 2147483647
<S>  New H14:  begidx <= 2147483647
<S>  New H15:  begidx <= endidx -> endidx >= - 2147483648 and endidx <= 
          2147483647
<S>  New H16:  begidx <= endidx -> begidx >= - 2147483648 and begidx <= 
          2147483647
<S>  New H18:  endidx >= - 2147483648 and endidx <= 2147483647
<S>  New H19:  begidx >= - 2147483648 and begidx <= 2147483647
-S-  Applied substitution rule convert8bitu_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H2:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(
          zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 
          character__last)
-S-  Applied substitution rule convert8bitu_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H2:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(
          zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 255)
-S-  Applied substitution rule convert8bitu_rules(13).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H7:  true
-S-  Applied substitution rule convert8bitu_rules(14).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H8:  true
-S-  Applied substitution rule convert8bitu_rules(23).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H9:  true
-S-  Applied substitution rule convert8bitu_rules(24).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H10:  true
-S-  Applied substitution rule convert8bitu_rules(29).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H3:  begidx >= 1
<S>  New H5:  endidx >= 1
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(zonefileline, [i___1]) 
          and element(zonefileline, [i___1]) <= 255)
-S-  Applied substitution rule convert8bitu_rules(30).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H4:  begidx <= 256
<S>  New H6:  endidx <= 256
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 
          255)
***  Proved C1:  begidx >= 1
     using hypothesis H3.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_6.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
%%%  Simplified H8 on reading formula in, to give:
     %%%  H8:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
---  Hypothesis H17 has been replaced by "true".  (It is already present, as 
          H13).
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H14).
---  Hypothesis H25 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H26 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
%%%  Simplified C8 on reading formula in, to give:
     %%%  C8:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
***  Proved C1:  begidx >= 1
     using hypothesis H1.
***  Proved C2:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 
          unsigned_types__max_8bit_val
     using hypothesis H27.
***  Proved C3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
     using hypothesis H3.
***  Proved C4:  begidx >= rr_type__linelengthindex__first
     using hypothesis H4.
***  Proved C5:  begidx <= rr_type__linelengthindex__last
     using hypothesis H5.
***  Proved C6:  endidx >= rr_type__linelengthindex__first
     using hypothesis H6.
***  Proved C7:  endidx <= rr_type__linelengthindex__last
     using hypothesis H7.
***  Proved C8:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
     using hypothesis H8.
***  Proved C9:  loop__1__i + 1 >= integer__first
     using hypothesis H9.
***  Proved C11:  loop__1__i + 1 >= begidx
     using hypothesis H11.
-S-  Applied substitution rule convert8bitu_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H10:  loop__1__i <= 2147483647
<S>  New C10:  loop__1__i <= 2147483646
>>>  Restructured hypothesis H27 into:
     >>>  H27:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 
          unsigned_types__max_8bit_val
>>>  Restructured hypothesis H28 into:
     >>>  H28:  loop__1__i <> endidx
-S-  Applied substitution rule convert8bitu_rules(1).
     This was achieved by replacing all occurrences of 
          unsigned_types__max_8bit_val by:
          255.
<S>  New H2:  tmpval <= 255
<S>  New H27:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 255
-S-  Applied substitution rule convert8bitu_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H9:  loop__1__i >= - 2147483648
-S-  Applied substitution rule convert8bitu_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H23:  10 * tmpval >= - 2147483648
-S-  Applied substitution rule convert8bitu_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H24:  10 * tmpval <= 2147483647
-S-  Applied substitution rule convert8bitu_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(
          zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 
          character__last)
-S-  Applied substitution rule convert8bitu_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(
          zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 255)
-S-  Applied substitution rule convert8bitu_rules(13).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H13:  element(zonefileline, [loop__1__i]) >= 48
<S>  New H19:  tmpval >= 0
<S>  New H21:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) >= 0
-S-  Applied substitution rule convert8bitu_rules(14).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H14:  element(zonefileline, [loop__1__i]) <= 2147483695
<S>  New H20:  tmpval <= 2147483647
<S>  New H22:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 
          2147483647
-S-  Applied substitution rule convert8bitu_rules(29).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H4:  begidx >= 1
<S>  New H6:  endidx >= 1
<S>  New H15:  loop__1__i >= 1
<S>  New H3:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(zonefileline, [i___1]) 
          and element(zonefileline, [i___1]) <= 255)
-S-  Applied substitution rule convert8bitu_rules(30).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H5:  begidx <= 256
<S>  New H7:  endidx <= 256
<S>  New H16:  loop__1__i <= 256
<S>  New H3:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 
          255)
%%%  Hypotheses H12 & H28 together imply that
          loop__1__i < endidx.
     H12 & H28 have therefore been deleted and a new H29 added to this effect.
***  Proved C12:  loop__1__i + 1 <= endidx
     via its standard form, which is:
     Std.Fm C12:  endidx - loop__1__i > 0
     using hypothesis H29.
***  Proved C10:  loop__1__i <= 2147483646
     using hypothesis H16.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_7.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
%%%  Simplified H8 on reading formula in, to give:
     %%%  H8:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
***  Proved C3:  loop__1__i >= rr_type__linelengthindex__first
     using hypotheses H4 & H11.
***  Proved C4:  loop__1__i <= rr_type__linelengthindex__last
     using hypotheses H7 & H12.
-S-  Applied substitution rule convert8bitu_rules(13).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New C1:  element(zonefileline, [loop__1__i]) >= 48
-S-  Applied substitution rule convert8bitu_rules(14).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New C2:  element(zonefileline, [loop__1__i]) <= 2147483695
***  Proved C1:  element(zonefileline, [loop__1__i]) >= 48
     using hypotheses H8, H11 & H12.
***  Proved C2:  element(zonefileline, [loop__1__i]) <= 2147483695
     using hypotheses H8, H11 & H12.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_8.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
%%%  Simplified H8 on reading formula in, to give:
     %%%  H8:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
---  Hypothesis H17 has been replaced by "true".  (It is already present, as 
          H13).
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H14).
-S-  Applied substitution rule convert8bitu_rules(13).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H13:  element(zonefileline, [loop__1__i]) >= 48
<S>  New H19:  tmpval >= 0
<S>  New C1:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) >= 0
-S-  Applied substitution rule convert8bitu_rules(14).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H14:  element(zonefileline, [loop__1__i]) <= 2147483695
<S>  New H20:  tmpval <= 2147483647
<S>  New C2:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 
          2147483647
-S-  Applied substitution rule convert8bitu_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New C3:  10 * tmpval >= - 2147483648
-S-  Applied substitution rule convert8bitu_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New C4:  10 * tmpval <= 2147483647
***  Proved C3:  10 * tmpval >= - 2147483648
     using hypothesis H19.
-S-  Applied substitution rule convert8bitu_rules(1).
     This was achieved by replacing all occurrences of 
          unsigned_types__max_8bit_val by:
          255.
<S>  New H2:  tmpval <= 255
-S-  Applied substitution rule convert8bitu_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H9:  loop__1__i >= - 2147483648
-S-  Applied substitution rule convert8bitu_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H10:  loop__1__i <= 2147483647
-S-  Applied substitution rule convert8bitu_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(
          zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 
          character__last)
-S-  Applied substitution rule convert8bitu_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(
          zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 255)
-S-  Applied substitution rule convert8bitu_rules(29).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H4:  begidx >= 1
<S>  New H6:  endidx >= 1
<S>  New H15:  loop__1__i >= 1
<S>  New H3:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(zonefileline, [i___1]) 
          and element(zonefileline, [i___1]) <= 255)
-S-  Applied substitution rule convert8bitu_rules(30).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H5:  begidx <= 256
<S>  New H7:  endidx <= 256
<S>  New H16:  loop__1__i <= 256
<S>  New H3:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 
          255)
***  Proved C1:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) >= 0
     via its standard form, which is:
     Std.Fm C1:  - 48 + (10 * tmpval + element(zonefileline, [loop__1__i])) >= 0
     using hypotheses H13 & H19.
***  Proved C4:  10 * tmpval <= 2147483647
     using hypothesis H2.
---  Eliminated hypothesis H17 (true-hypothesis).
---  Eliminated hypothesis H18 (true-hypothesis).
---  Eliminated hypothesis H4 (duplicate of H1).
---  Eliminated hypothesis H9 (redundant, given H15).
---  Eliminated hypothesis H10 (redundant, given H16).
---  Eliminated hypothesis H20 (redundant, given H2).
***  Proved C2:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 
          2147483647
     using hypotheses H2, H8, H11 & H12.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_9.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H8)
          .
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H7)
          .
---  Hypothesis H22 has been replaced by "true".  (It is already present, as H8)
          .
***  Proved C1:  0 >= unsigned_types__unsigned8__first
     using hypothesis H9.
***  Proved C2:  0 <= unsigned_types__unsigned8__last
     using hypothesis H10.
***  Proved C3:  0 >= unsigned_types__unsigned8__first
     using hypothesis H9.
***  Proved C4:  0 <= unsigned_types__unsigned8__last
     using hypothesis H10.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_10.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
%%%  Simplified H8 on reading formula in, to give:
     %%%  H8:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
---  Hypothesis H17 has been replaced by "true".  (It is already present, as 
          H13).
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H14).
---  Hypothesis H25 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H26 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H22).
-S-  Applied substitution rule convert8bitu_rules(23).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New C1:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) >= 0
<S>  New C3:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) >= 0
-S-  Applied substitution rule convert8bitu_rules(24).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New C2:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 255
<S>  New C4:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 255
>>>  Restructured hypothesis H30 into:
     >>>  H30:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 
          unsigned_types__max_8bit_val
-S-  Applied substitution rule convert8bitu_rules(1).
     This was achieved by replacing all occurrences of 
          unsigned_types__max_8bit_val by:
          255.
<S>  New H2:  tmpval <= 255
<S>  New H27:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) > 255
<S>  New H30:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 255
-S-  Applied substitution rule convert8bitu_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H9:  loop__1__i >= - 2147483648
-S-  Applied substitution rule convert8bitu_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H10:  loop__1__i <= 2147483647
-S-  Applied substitution rule convert8bitu_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H23:  10 * tmpval >= - 2147483648
-S-  Applied substitution rule convert8bitu_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H24:  10 * tmpval <= 2147483647
-S-  Applied substitution rule convert8bitu_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(
          zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 
          character__last)
-S-  Applied substitution rule convert8bitu_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(
          zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 255)
-S-  Applied substitution rule convert8bitu_rules(13).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H13:  element(zonefileline, [loop__1__i]) >= 48
<S>  New H19:  tmpval >= 0
<S>  New H21:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) >= 0
-S-  Applied substitution rule convert8bitu_rules(14).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H14:  element(zonefileline, [loop__1__i]) <= 2147483695
<S>  New H20:  tmpval <= 2147483647
<S>  New H22:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 
          2147483647
-S-  Applied substitution rule convert8bitu_rules(29).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H4:  begidx >= 1
<S>  New H6:  endidx >= 1
<S>  New H15:  loop__1__i >= 1
<S>  New H3:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(zonefileline, [i___1]) 
          and element(zonefileline, [i___1]) <= 255)
-S-  Applied substitution rule convert8bitu_rules(30).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H5:  begidx <= 256
<S>  New H7:  endidx <= 256
<S>  New H16:  loop__1__i <= 256
<S>  New H3:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 
          255)
***  Proved C1:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) >= 0
     using hypothesis H21.
***  Proved C3:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) >= 0
     using hypothesis H21.
***  Proved C2:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 255
     using hypothesis H30.
***  Proved C4:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 255
     using hypothesis H30.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_11.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(zonefileline, [i___1]) and element(zonefileline, [i___1]) 
          <= character__last)
%%%  Simplified H8 on reading formula in, to give:
     %%%  H8:  for_all(i_ : integer, begidx <= i_ and i_ <= endidx -> 48 <= 
          element(zonefileline, [i_]) and element(zonefileline, [i_]) <= 57)
---  Hypothesis H17 has been replaced by "true".  (It is already present, as 
          H13).
---  Hypothesis H18 has been replaced by "true".  (It is already present, as 
          H14).
---  Hypothesis H25 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H26 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H30 has been replaced by "true".  (It is already present, as 
          H22).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H22).
-S-  Applied substitution rule convert8bitu_rules(23).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New C1:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) >= 0
<S>  New C3:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) >= 0
-S-  Applied substitution rule convert8bitu_rules(24).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New C2:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 255
<S>  New C4:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 255
>>>  Restructured hypothesis H27 into:
     >>>  H27:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 
          unsigned_types__max_8bit_val
-S-  Applied substitution rule convert8bitu_rules(1).
     This was achieved by replacing all occurrences of 
          unsigned_types__max_8bit_val by:
          255.
<S>  New H2:  tmpval <= 255
<S>  New H27:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 255
-S-  Applied substitution rule convert8bitu_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H9:  loop__1__i >= - 2147483648
-S-  Applied substitution rule convert8bitu_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H10:  loop__1__i <= 2147483647
-S-  Applied substitution rule convert8bitu_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H23:  10 * tmpval >= - 2147483648
-S-  Applied substitution rule convert8bitu_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H24:  10 * tmpval <= 2147483647
-S-  Applied substitution rule convert8bitu_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(
          zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 
          character__last)
-S-  Applied substitution rule convert8bitu_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H3:  for_all(i___1 : integer, rr_type__linelengthindex__first <= i___1 
          and i___1 <= rr_type__linelengthindex__last -> 0 <= element(
          zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 255)
-S-  Applied substitution rule convert8bitu_rules(13).
     This was achieved by replacing all occurrences of natural__first by:
          0.
<S>  New H13:  element(zonefileline, [loop__1__i]) >= 48
<S>  New H19:  tmpval >= 0
<S>  New H21:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) >= 0
-S-  Applied substitution rule convert8bitu_rules(14).
     This was achieved by replacing all occurrences of natural__last by:
          2147483647.
<S>  New H14:  element(zonefileline, [loop__1__i]) <= 2147483695
<S>  New H20:  tmpval <= 2147483647
<S>  New H22:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 
          2147483647
-S-  Applied substitution rule convert8bitu_rules(29).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H4:  begidx >= 1
<S>  New H6:  endidx >= 1
<S>  New H15:  loop__1__i >= 1
<S>  New H3:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(zonefileline, [i___1]) 
          and element(zonefileline, [i___1]) <= 255)
-S-  Applied substitution rule convert8bitu_rules(30).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H5:  begidx <= 256
<S>  New H7:  endidx <= 256
<S>  New H16:  loop__1__i <= 256
<S>  New H3:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(zonefileline, [i___1]) and element(zonefileline, [i___1]) <= 
          255)
***  Proved C1:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) >= 0
     using hypothesis H21.
***  Proved C3:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) >= 0
     using hypothesis H21.
***  Proved C2:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 255
     using hypothesis H27.
***  Proved C4:  10 * tmpval + (element(zonefileline, [loop__1__i]) - 48) <= 255
     using hypothesis H27.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_12.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_13.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_14.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_15.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_16.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_convert8bitunsigned_17.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.

