let I, J be Program of SCM+FSA ; :: thesis: dom I c= dom (I ';' J)
dom (I ';' J) = (dom (Directed I)) \/ (dom (ProgramPart (Relocated J,(card I)))) by FUNCT_4:def 1
.= (dom I) \/ (dom (ProgramPart (Relocated J,(card I)))) by FUNCT_4:105 ;
hence dom I c= dom (I ';' J) by XBOOLE_1:7; :: thesis: verum