proposition: Lemma msetB1K a A : a \in A -> a +` (A `\ a) = A.
proof: Proof. move=> aA; apply/msetP=> x; rewrite !msetE subnKC //=. by have [->|//] := altP eqP; rewrite mset_gt0. Qed.
imports: mathcomp(ssreflect ssrbool ssrnat eqtype ssrfun seq) mathcomp(choice path finset finfun fintype bigop tuple) finmap