let I, J be Program of SCM+FSA ; :: thesis: card (I ';' J) = (card I) + (card J)
A1: ( card (dom (I ';' J)) = card (I ';' J) & card (dom I) = card I & card (dom J) = card J ) by CARD_1:104;
A2: card (dom (ProgramPart (Relocated J,(card I)))) = card (ProgramPart (Relocated J,(card I))) by CARD_1:104
.= card J by Th17
.= card (dom J) by CARD_1:104 ;
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 card (I ';' J) = (card I) + (card J) by A1, A2, Th16, CARD_2:53; :: thesis: verum