reserve x,y,y1,y2 for set,
  D for non empty set,
  d,d1,d2,d3 for Element of D,
  F,G,H,H1,H2 for FinSequence of D,
  f,f1,f2 for sequence of D,
  g for BinOp of D,
  k,n,i,l for Nat,
  P for Permutation of dom F;

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;
