let I be Program of SCM+FSA ; :: thesis: intloc 0 in dom (Initialized I)
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 ;
intloc 0 in {(intloc 0 )} by TARSKI:def 1;
then intloc 0 in (dom I) \/ {(intloc 0 )} by XBOOLE_0:def 3;
hence intloc 0 in dom (Initialized I) by A3, XBOOLE_0:def 3; :: thesis: verum