let a be Int-Location ; :: thesis: for I, J being Program of SCM+FSA holds
( insloc 0 in dom (if=0 a,I,J) & insloc 1 in dom (if=0 a,I,J) & insloc 0 in dom (if>0 a,I,J) & insloc 1 in dom (if>0 a,I,J) )
let I, J be Program of SCM+FSA ; :: thesis: ( insloc 0 in dom (if=0 a,I,J) & insloc 1 in dom (if=0 a,I,J) & insloc 0 in dom (if>0 a,I,J) & insloc 1 in dom (if>0 a,I,J) )
set i = a =0_goto (insloc ((card J) + 3));
if=0 a,I,J = ((((a =0_goto (insloc ((card J) + 3))) ';' J) ';' (Goto (insloc ((card I) + 1)))) ';' I) ';' (Stop SCM+FSA ) by SCMFSA8B:def 1
.= (((a =0_goto (insloc ((card J) + 3))) ';' J) ';' (Goto (insloc ((card I) + 1)))) ';' (I ';' (Stop SCM+FSA )) by SCMFSA6A:67
.= ((a =0_goto (insloc ((card J) + 3))) ';' J) ';' ((Goto (insloc ((card I) + 1))) ';' (I ';' (Stop SCM+FSA ))) by SCMFSA6A:67
.= (a =0_goto (insloc ((card J) + 3))) ';' (J ';' ((Goto (insloc ((card I) + 1))) ';' (I ';' (Stop SCM+FSA )))) by SCMFSA6A:71
.= (Macro (a =0_goto (insloc ((card J) + 3)))) ';' (J ';' ((Goto (insloc ((card I) + 1))) ';' (I ';' (Stop SCM+FSA )))) ;
then A1: dom (Macro (a =0_goto (insloc ((card J) + 3)))) c= dom (if=0 a,I,J) by SCMFSA6A:56;
dom (Macro (a =0_goto (insloc ((card J) + 3)))) = {(insloc 0 ),(insloc 1)} by SCMFSA7B:4;
then ( insloc 0 in dom (Macro (a =0_goto (insloc ((card J) + 3)))) & insloc 1 in dom (Macro (a =0_goto (insloc ((card J) + 3)))) ) by TARSKI:def 2;
hence ( insloc 0 in dom (if=0 a,I,J) & insloc 1 in dom (if=0 a,I,J) ) by A1; :: thesis: ( insloc 0 in dom (if>0 a,I,J) & insloc 1 in dom (if>0 a,I,J) )
set i = a >0_goto (insloc ((card J) + 3));
if>0 a,I,J = ((((a >0_goto (insloc ((card J) + 3))) ';' J) ';' (Goto (insloc ((card I) + 1)))) ';' I) ';' (Stop SCM+FSA ) by SCMFSA8B:def 2
.= (((a >0_goto (insloc ((card J) + 3))) ';' J) ';' (Goto (insloc ((card I) + 1)))) ';' (I ';' (Stop SCM+FSA )) by SCMFSA6A:67
.= ((a >0_goto (insloc ((card J) + 3))) ';' J) ';' ((Goto (insloc ((card I) + 1))) ';' (I ';' (Stop SCM+FSA ))) by SCMFSA6A:67
.= (a >0_goto (insloc ((card J) + 3))) ';' (J ';' ((Goto (insloc ((card I) + 1))) ';' (I ';' (Stop SCM+FSA )))) by SCMFSA6A:71
.= (Macro (a >0_goto (insloc ((card J) + 3)))) ';' (J ';' ((Goto (insloc ((card I) + 1))) ';' (I ';' (Stop SCM+FSA )))) ;
then A2: dom (Macro (a >0_goto (insloc ((card J) + 3)))) c= dom (if>0 a,I,J) by SCMFSA6A:56;
dom (Macro (a >0_goto (insloc ((card J) + 3)))) = {(insloc 0 ),(insloc 1)} by SCMFSA7B:4;
then ( insloc 0 in dom (Macro (a >0_goto (insloc ((card J) + 3)))) & insloc 1 in dom (Macro (a >0_goto (insloc ((card J) + 3)))) ) by TARSKI:def 2;
hence ( insloc 0 in dom (if>0 a,I,J) & insloc 1 in dom (if>0 a,I,J) ) by A2; :: thesis: verum