let I be Program of SCMPDS ; :: thesis: IC (Initialized I) = inspos 0
dom (Start-At (inspos 0 )) = {(IC SCMPDS )} by FUNCOP_1:19;
then A1: IC SCMPDS in dom (Start-At (inspos 0 )) by TARSKI:def 1;
IC SCMPDS in dom (Initialized I) by Th7;
hence IC (Initialized I) = (I +* (Start-At (inspos 0 ))) . (IC SCMPDS ) by AMI_1:def 43
.= (Start-At (inspos 0 )) . (IC SCMPDS ) by A1, FUNCT_4:14
.= inspos 0 by FUNCOP_1:87 ;
:: thesis: verum