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
  (f1<++>f2) <##> f = (f1<##>f) <++> (f2<##>f)
proof
  set f3 = f1<##>f, f4 = f2<##>f, f5 = f1<++>f2;
A1: f1<##>f = f<##>f1 & f2<##>f = f<##>f2 by Th83;
  thus f5 <##> f = f <##> f5 by Th83
    .= f3 <++> f4 by A1,Th87;
end;
