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)),())) ";" (SubFrom ((intloc (1 + 1)),()))))),P,s)) . () = s . ()
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)),())) ";" (SubFrom ((intloc (1 + 1)),()))))),P,s)) . () = s . ()
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)),())) ";" (SubFrom ((intloc (1 + 1)),()))))),P,s)) . () = s . ()
hence (IExec ((if>0 ((intloc (4 + 1)),(Macro (SubFrom ((intloc (1 + 1)),(intloc (1 + 1))))),((AddTo ((intloc (3 + 1)),())) ";" (SubFrom ((intloc (1 + 1)),()))))),P,s)) . () = (IExec ((Macro (SubFrom ((intloc (1 + 1)),(intloc (1 + 1))))),P,s)) . () by SCM_HALT:44
.= (IExec ((Macro (SubFrom ((intloc (1 + 1)),(intloc (1 + 1))))),P,s)) . ()
.= (Exec ((SubFrom ((intloc (1 + 1)),(intloc (1 + 1)))),())) . () by SCMFSA6C:5
.= (Exec ((SubFrom ((intloc (1 + 1)),(intloc (1 + 1)))),())) . ()
.= () . () by SCMFSA_2:65
.= s . () 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)),())) ";" (SubFrom ((intloc (1 + 1)),()))))),P,s)) . () = s . ()
hence (IExec ((if>0 ((intloc (4 + 1)),(Macro (SubFrom ((intloc (1 + 1)),(intloc (1 + 1))))),((AddTo ((intloc (3 + 1)),())) ";" (SubFrom ((intloc (1 + 1)),()))))),P,s)) . () = (IExec (((AddTo ((intloc (3 + 1)),())) ";" (SubFrom ((intloc (1 + 1)),()))),P,s)) . () by SCM_HALT:44
.= (Exec ((SubFrom ((intloc (1 + 1)),())),(Exec ((AddTo ((intloc (3 + 1)),())),())))) . () by SCMFSA6C:9
.= (Exec ((AddTo ((intloc (3 + 1)),())),())) . () by SCMFSA_2:65
.= () . () by SCMFSA_2:64
.= s . () by SCMFSA_M:37 ;
:: thesis: verum
end;
end;