proposition: Lemma injm_proper A B : A \subset G -> B \subset G -> (f @* A \proper f @* B) = (A \proper B).
proof: Proof. move=> dA dB; rewrite -morphpre_invm -(morphpre_invm B). by rewrite morphpre_proper ?morphim_invm. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype finfun bigop finset fingroup)