theorem
  F is commutative associative & F is having_a_unity & F is
having_an_inverseOp & G is_distributive_wrt F implies G.(d,F$$(B,f)) = F $$(B,G
  [;](d,f))
proof
  assume that
A1: F is commutative associative & F is having_a_unity and
A2: F is having_an_inverseOp and
A3: G is_distributive_wrt F;
  set e = the_unity_wrt F;
  G.(d,e) = e by A1,A2,A3,FINSEQOP:66;
  hence thesis by A1,A3,Th12;
end;
