theorem
  F is commutative associative & F is having_a_unity implies F.(F$$(B,f)
  ,F$$(B,f9)) = F $$(B,F.:(f,f9))
proof
  set e = the_unity_wrt F;
  assume
A1: F is commutative & F is associative & F is having_a_unity;
  then
  F.(e,e) = e & for d1,d2,d3,d4 holds F.(F.(d1,d2),F.(d3,d4))= F.(F.(d1,d3
  ),F. (d2,d4)) by Lm3,SETWISEO:15;
  hence thesis by A1,Th9;
end;
