proposition: Lemma fsubset_leqif_cards A B : A `<=` B -> (#|` A| <= #|` B| ?= iff (A == B))%N.
proof: Proof. rewrite -!(@card_fsub (A `|` B)) // -(@subset_fsubE (A `|` B)) //. by move=> /subset_leqif_cards; rewrite (inj_in_eq (@fsub_inj _)) -?topredE /=. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrnat eqtype ssrfun seq) mathcomp(choice path finset finfun fintype bigop)