 reserve R for 1-sorted;
 reserve X,Y for Subset of R;
 reserve R for finite 1-sorted;
 reserve X,Y for Subset of R;

theorem LemmaCard:
  card (X \/ Y) = card Y iff X c= Y
  proof
    X c= X \/ Y & Y c= X \/ Y by XBOOLE_1:7;
    hence card (X \/ Y) = card Y implies X c= Y by CARD_2:102;
    assume X c= Y;
    hence thesis by XBOOLE_1:12;
  end;
