Section BaseSetMulProp.
(* Properties of the purely multiplicative structure. *)
Variable gT : baseFinGroupType.
Implicit Types A B C D : {set gT}.
Implicit Type x y z : gT.
(* Set product. We already have all the pregroup identities, so we *)
(* only need to add the monotonicity rules.                        *)
(* Conjugates. *)

Lemma mem_classes x A : x \in A -> x ^: A \in classes A.