reserve a,x,y for object, A,B for set,
  l,m,n for Nat;

theorem
  for f,g,h being Function st rng f misses dom g holds (h +* g)*f = h*f
proof
  let f,g,h be Function;
  assume
A1: rng f misses dom g;
  thus (h +* g)*f = (h*f) +* (g*f) by Th10
    .= h*f +* {} by A1,RELAT_1:44
    .= h*f;
end;
