let I be Program of SCMPDS ; :: thesis: IC SCMPDS in dom (Initialized I)
A1: dom (Initialized I) = (dom I) \/ (dom (Start-At (inspos 0 ))) by FUNCT_4:def 1;
dom (Start-At (inspos 0 )) = {(IC SCMPDS )} by FUNCOP_1:19;
then IC SCMPDS in dom (Start-At (inspos 0 )) by TARSKI:def 1;
hence IC SCMPDS in dom (Initialized I) by A1, XBOOLE_0:def 3; :: thesis: verum