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