let p be PartState of SCM+FSA; :: thesis: IC in dom (Initialized p)
A1: Initialized p = (p +* ((intloc 0) .--> 1)) +* (Start-At (0,SCM+FSA)) by FUNCT_4:15;
dom (Start-At (0,SCM+FSA)) = {(IC )} by FUNCOP_1:19;
then ( dom (Initialized p) = (dom (p +* ((intloc 0) .--> 1))) \/ (dom (Start-At (0,SCM+FSA))) & IC in dom (Start-At (0,SCM+FSA)) ) by A1, FUNCT_4:def 1, TARSKI:def 1;
hence IC in dom (Initialized p) by XBOOLE_0:def 3; :: thesis: verum