theorem
  F is associative & F is having_a_unity & F is having_an_inverseOp & G
  is_distributive_wrt F implies G[;](d,id D).(F"**"p) = F "**"(G[;](d,id D)*p)
proof
  assume that
A1: F is associative and
A2: F is having_a_unity and
A3: F is having_an_inverseOp and
A4: G is_distributive_wrt F;
  set e = the_unity_wrt F;
  set u = G[;](d,id D);
  u is_distributive_wrt F by A4,FINSEQOP:54;
  then
A5: for d1,d2 holds u.(F.(d1,d2)) = F.(u.d1,u.d2);
  G[;](d,id D).e = e by A1,A2,A3,A4,FINSEQOP:69;
  hence thesis by A2,A5,Th28;
end;
