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 )} & dom (Start-At 0 ,SCM+FSA ) = {(IC SCM+FSA )} ) by FUNCOP_1:19;
assume A2: x in dom (Initialized I) ; :: thesis: ( x in dom I or x = intloc 0 or x = IC SCM+FSA )
dom (Initialized I) = (dom (I +* ((intloc 0 ) .--> 1))) \/ (dom (Start-At 0 ,SCM+FSA )) by FUNCT_4:def 1
.= ((dom I) \/ {(intloc 0 )}) \/ {(IC SCM+FSA )} by A1, FUNCT_4:def 1 ;
then ( x in (dom I) \/ {(intloc 0 )} or x in {(IC SCM+FSA )} ) by A2, 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