let I be Program of SCM+FSA ; :: thesis: for x being set holds
( not x in dom (Initialized I) or x in dom I or x = intloc 0 or x = IC SCM+FSA )
let x be set ; :: thesis: ( not x in dom (Initialized I) or x in dom I or x = intloc 0 or x = IC SCM+FSA )
A1: dom ((intloc 0 ) .--> 1) = {(intloc 0 )} by FUNCOP_1:19;
A2: dom (Start-At (insloc 0 )) = {(IC SCM+FSA )} by FUNCOP_1:19;
A3: dom (Initialized I) = (dom (I +* ((intloc 0 ) .--> 1))) \/ (dom (Start-At (insloc 0 ))) by FUNCT_4:def 1
.= ((dom I) \/ {(intloc 0 )}) \/ {(IC SCM+FSA )} by A1, A2, FUNCT_4:def 1 ;
assume x in dom (Initialized I) ; :: thesis: ( x in dom I or x = intloc 0 or x = IC SCM+FSA )
then ( x in (dom I) \/ {(intloc 0 )} or x in {(IC SCM+FSA )} ) by A3, XBOOLE_0:def 3;
then ( x in dom I or x in {(intloc 0 )} or x in {(IC SCM+FSA )} ) by XBOOLE_0:def 3;
hence ( x in dom I or x = intloc 0 or x = IC SCM+FSA ) by TARSKI:def 1; :: thesis: verum