let s be State of SCM+FSA; :: thesis: for P being Instruction-Sequence of SCM+FSA holds
( (IExec (((((intloc (4 + 1)) := ((fsloc 0),(intloc (1 + 1)))) ";" (SubFrom ((intloc (4 + 1)),(intloc (5 + 1))))) ";" (if>0 ((intloc (4 + 1)),(Macro (SubFrom ((intloc (1 + 1)),(intloc (1 + 1))))),((AddTo ((intloc (3 + 1)),(intloc 0))) ";" (SubFrom ((intloc (1 + 1)),(intloc 0))))))),P,s)) . (intloc (1 + 1)) < s . (intloc (1 + 1)) or (IExec (((((intloc (4 + 1)) := ((fsloc 0),(intloc (1 + 1)))) ";" (SubFrom ((intloc (4 + 1)),(intloc (5 + 1))))) ";" (if>0 ((intloc (4 + 1)),(Macro (SubFrom ((intloc (1 + 1)),(intloc (1 + 1))))),((AddTo ((intloc (3 + 1)),(intloc 0))) ";" (SubFrom ((intloc (1 + 1)),(intloc 0))))))),P,s)) . (intloc (1 + 1)) <= 0 )
let P be Instruction-Sequence of SCM+FSA; :: thesis: ( (IExec (((((intloc (4 + 1)) := ((fsloc 0),(intloc (1 + 1)))) ";" (SubFrom ((intloc (4 + 1)),(intloc (5 + 1))))) ";" (if>0 ((intloc (4 + 1)),(Macro (SubFrom ((intloc (1 + 1)),(intloc (1 + 1))))),((AddTo ((intloc (3 + 1)),(intloc 0))) ";" (SubFrom ((intloc (1 + 1)),(intloc 0))))))),P,s)) . (intloc (1 + 1)) < s . (intloc (1 + 1)) or (IExec (((((intloc (4 + 1)) := ((fsloc 0),(intloc (1 + 1)))) ";" (SubFrom ((intloc (4 + 1)),(intloc (5 + 1))))) ";" (if>0 ((intloc (4 + 1)),(Macro (SubFrom ((intloc (1 + 1)),(intloc (1 + 1))))),((AddTo ((intloc (3 + 1)),(intloc 0))) ";" (SubFrom ((intloc (1 + 1)),(intloc 0))))))),P,s)) . (intloc (1 + 1)) <= 0 )
set s0 = Initialized s;
set s1 = Exec (((intloc (4 + 1)) := ((fsloc 0),(intloc (1 + 1)))),(Initialized s));
set s2 = IExec ((((intloc (4 + 1)) := ((fsloc 0),(intloc (1 + 1)))) ";" (SubFrom ((intloc (4 + 1)),(intloc (5 + 1))))),P,s);
A1: intloc (4 + 1) <> intloc (1 + 1) by SCMFSA_2:101;
A2: (IExec ((((intloc (4 + 1)) := ((fsloc 0),(intloc (1 + 1)))) ";" (SubFrom ((intloc (4 + 1)),(intloc (5 + 1))))),P,s)) . (intloc (1 + 1)) = (Exec ((SubFrom ((intloc (4 + 1)),(intloc (5 + 1)))),(Exec (((intloc (4 + 1)) := ((fsloc 0),(intloc (1 + 1)))),(Initialized s))))) . (intloc (1 + 1)) by SCMFSA6C:8
.= (Exec (((intloc (4 + 1)) := ((fsloc 0),(intloc (1 + 1)))),(Initialized s))) . (intloc (1 + 1)) by A1, SCMFSA_2:65
.= (Initialized s) . (intloc (1 + 1)) by A1, SCMFSA_2:72
.= s . (intloc (1 + 1)) by SCMFSA_M:37 ;