*****************************************************************************
                       Semantic Analysis of SPARK Text
    Examiner Pro Edition, Version 9.1.0, Build Date 20101119, Build 19039
             Copyright (C) 2010 Altran Praxis Limited, Bath, U.K.
*****************************************************************************


CREATED 22-SEP-2011, 11:10:50  SIMPLIFIED 22-SEP-2011, 11:10:51

SPARK Simplifier Pro Edition, Version 9.1.0, Build Date 20101119, Build 19039
Copyright (C) 2010 Altran Praxis Limited, Bath, U.K.

procedure Loop_Invariant.Proc2




For path(s) from start to run-time check associated with statement of line 18:

procedure_proc2_1.
*** true .          /* all conclusions proved */


For path(s) from start to run-time check associated with statement of line 19:

procedure_proc2_2.
*** true .          /* all conclusions proved */


For path(s) from start to run-time check associated with statement of line 19:

procedure_proc2_3.
*** true .          /* all conclusions proved */


For path(s) from start to assertion of line 19:

procedure_proc2_4.
*** true .          /* all conclusions proved */


For path(s) from assertion of line 23 to assertion of line 19:

procedure_proc2_5.
*** true .          /* all conclusions proved */


For path(s) from assertion of line 19 to run-time check associated with 
          statement of line 22:

procedure_proc2_6.
*** true .          /* all conclusions proved */


For path(s) from assertion of line 19 to assertion of line 23:

procedure_proc2_7.
H1:    a <= 2147483647 .
H2:    b >= 0 .
H3:    b <= 4294967295 .
H4:    loop__1__i <= 2147483647 .
H5:    loop__1__i >= 1 .
H6:    loop__1__i <= a .
H7:    (loop__1__i - 1) * b mod 4294967296 >= 0 .
H8:    (loop__1__i - 1) * b mod 4294967296 <= 4294967295 .
H9:    ((loop__1__i - 1) * b mod 4294967296 + b) mod 4294967296 >= 0 .
H10:   ((loop__1__i - 1) * b mod 4294967296 + b) mod 4294967296 <= 4294967295 .
H11:   integer__size >= 0 .
H12:   natural__size >= 0 .
H13:   word32__size >= 0 .
       ->
C1:    loop__1__i * b mod 4294967296 = ((loop__1__i - 1) * b mod 4294967296 + b)
           mod 4294967296 .


For path(s) from start to finish:

procedure_proc2_8.
*** true .          /* all conclusions proved */


For path(s) from assertion of line 23 to finish:

procedure_proc2_9.
*** true .          /* all conclusions proved */