let I be Program of SCM+FSA ; :: thesis: intloc 0 in dom (Initialized I)
A1: ( dom ((intloc 0 ) .--> 1) = {(intloc 0 )} & dom (Start-At 0 ,SCM+FSA ) = {(IC SCM+FSA )} ) by FUNCOP_1:19;
intloc 0 in {(intloc 0 )} by TARSKI:def 1;
then A2: intloc 0 in (dom I) \/ {(intloc 0 )} by XBOOLE_0:def 3;
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 ;
hence intloc 0 in dom (Initialized I) by A2, XBOOLE_0:def 3; :: thesis: verum