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