let P be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA holds (IExec ((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)) . (fsloc 0) = s . (fsloc 0)
let s be State of SCM+FSA; :: thesis: (IExec ((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)) . (fsloc 0) = s . (fsloc 0)
set s0 = Initialized s;

per cases ( s . (intloc (4 + 1)) > 0 or s . (intloc (4 + 1)) <= 0 ) ;

suppose s . (intloc (4 + 1)) > 0 ; :: thesis: (IExec ((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)) . (fsloc 0) = s . (fsloc 0)

hence (IExec ((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)) . (fsloc 0) = (IExec ((Macro (SubFrom ((intloc (1 + 1)),(intloc (1 + 1))))),P,s)) . (fsloc 0) by SCM_HALT:44
.= (IExec ((Macro (SubFrom ((intloc (1 + 1)),(intloc (1 + 1))))),P,s)) . (fsloc 0)
.= (Exec ((SubFrom ((intloc (1 + 1)),(intloc (1 + 1)))),(Initialized s))) . (fsloc 0) by SCMFSA6C:5
.= (Exec ((SubFrom ((intloc (1 + 1)),(intloc (1 + 1)))),(Initialized s))) . (fsloc 0)
.= (Initialized s) . (fsloc 0) by SCMFSA_2:65
.= s . (fsloc 0) by SCMFSA_M:37 ;
:: thesis: verum

end;

suppose s . (intloc (4 + 1)) <= 0 ; :: thesis: (IExec ((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)) . (fsloc 0) = s . (fsloc 0)

hence (IExec ((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)) . (fsloc 0) = (IExec (((AddTo ((intloc (3 + 1)),(intloc 0))) ";" (SubFrom ((intloc (1 + 1)),(intloc 0)))),P,s)) . (fsloc 0) by SCM_HALT:44
.= (Exec ((SubFrom ((intloc (1 + 1)),(intloc 0))),(Exec ((AddTo ((intloc (3 + 1)),(intloc 0))),(Initialized s))))) . (fsloc 0) by SCMFSA6C:9
.= (Exec ((AddTo ((intloc (3 + 1)),(intloc 0))),(Initialized s))) . (fsloc 0) by SCMFSA_2:65
.= (Initialized s) . (fsloc 0) by SCMFSA_2:64
.= s . (fsloc 0) by SCMFSA_M:37 ;
:: thesis: verum

end;

end;