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