theorem
  X c= Y implies X --> a c= Y --> a
proof
  assume
A2: X c= Y;
A3: now
    let x be object;
    assume
A4: x in dom(X --> a);
    then (X --> a).x = a by FUNCOP_1:7;
    hence (X --> a).x = (Y --> a).x by A2,A4,FUNCOP_1:7;
  end;
  dom(Y --> a) = Y;
  hence thesis by A2,A3,GRFUNC_1:2;
end;
