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.                        *)

Lemma mulsgP A B x :
reflect (imset2_spec mulg (mem A) (fun _ => mem B) x) (x \in A * B).