reserve A,B for Ordinal,
  K,M,N for Cardinal,
  x,x1,x2,y,y1,y2,z,u for object,X,Y,Z,X1,X2, Y1,Y2 for set,
  f,g for Function;
reserve m,n for Nat;

theorem
  (card X c= card Y or card X in card Y) & Y is finite implies X is finite
proof
  assume that
A1: card X c= card Y or card X in card Y and
A2: Y is finite;
  card X c= card Y by A1,ORDINAL1:def 2;
  hence thesis by A2;
end;
