let I be Program of SCM+FSA ; :: thesis: dom (Initialized I) = ((dom I) \/ {(intloc 0 )}) \/ {(IC SCM+FSA )}
A1: ( dom ((intloc 0 ) .--> 1) = {(intloc 0 )} & dom (Start-At 0 ,SCM+FSA ) = {(IC SCM+FSA )} ) by FUNCOP_1:19;
thus dom (Initialized I) = (dom (I +* ((intloc 0 ) .--> 1))) \/ (dom (Start-At 0 ,SCM+FSA )) by FUNCT_4:def 1
.= ((dom I) \/ {(intloc 0 )}) \/ {(IC SCM+FSA )} by A1, FUNCT_4:def 1 ; :: thesis: verum