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;

theorem
  Card (X --> Y) = X --> card Y
proof
A1: dom Card (X --> Y) = dom(X --> Y) by Def2;
  then
A2: dom Card (X --> Y) = X;
  now
    let x be object;
    assume
A4: x in X;
    then
A5: Card (X --> Y).x = card ((X --> Y).x) by A1,Def2;
    (X --> card Y).x = card Y by A4,FUNCOP_1:7;
    hence Card (X --> Y).x = (X --> card Y).x by A4,A5,FUNCOP_1:7;
  end;
  hence thesis by A2;
end;
