theorem
  for F being Function of X,Y, x being Element of X,
      z being Element of Z holds [:F,id Z:].(x,z) = [F.x,z]
proof
  let F be Function of X,Y, x be Element of X, z be Element of Z;
  thus [:F,id Z:].(x,z) = [F.x, (id Z).z] by FUNCT_3:75
    .= [F.x,z];
end;
