let I be Program of SCMPDS ; :: thesis: IC (Initialized I) = 0
dom (Start-At 0 ,SCMPDS ) = {(IC SCMPDS )} by FUNCOP_1:19;
then A1: IC SCMPDS in dom (Start-At 0 ,SCMPDS ) by TARSKI:def 1;
thus IC (Initialized I) = (I +* (Start-At 0 ,SCMPDS )) . (IC SCMPDS )
.= (Start-At 0 ,SCMPDS ) . (IC SCMPDS ) by A1, FUNCT_4:14
.= 0 by FUNCOP_1:87 ; :: thesis: verum