reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve ff for Cardinal-Function;
reserve F,G for Cardinal-Function;
reserve A,B for set;
reserve A,B for Ordinal;

theorem Th85:
  card X = card Y iff nextcard X = nextcard Y
proof
  thus card X = card Y implies nextcard X = nextcard Y by CARD_1:16;
  assume that
A1: nextcard X = nextcard Y and
A2: card X <> card Y;
  card X in card Y or card Y in card X by A2,ORDINAL1:14;
  then nextcard X c= card Y & card Y in nextcard Y or
  nextcard Y c= card X & card X in nextcard X by CARD_1:def 3;
  hence thesis by A1,ORDINAL1:12;
end;
