theorem
  (g is having_a_unity or len F >= 1) & g is associative commutative & F
  is one-to-one & G is one-to-one & rng F = rng G implies g "**" F = g "**" G
proof
  len F >= 1 or len F = 0 by NAT_1:14;
  hence thesis by Lm9,Lm10;
end;
