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