reserve x, y for object, X, X1, X2 for set;
reserve Y, Y1, Y2 for complex-functions-membered set,
  c, c1, c2 for Complex,
  f for PartFunc of X,Y,
  f1 for PartFunc of X1,Y1,
  f2 for PartFunc of X2, Y2,
  g, h, k for complex-valued Function;

theorem
  </></>f = f
proof
  set f1 = </>f;
A1: dom f1 = dom f by Def35;
  hence
A2: dom </>f1 = dom f by Def35;
  let x be object;
  assume
A3: x in dom </>f1;
  hence (</>f1).x = (f1.x)" by Def35
    .= (f.x)"" by A1,A2,A3,Def35
    .= f.x;
end;
