theorem
  (g is having_a_unity or len F >= 1) & g is associative & g is
  commutative implies g "**" F = g $$(findom F,(NAT-->the_unity_wrt g)+*F)
proof
  len F = 0 or len F >= 1 by NAT_1:14;
  hence thesis by Lm1,Lm2;
end;
