proposition: Lemma setD1K a A : a \in A -> a |: (A :\ a) = A.
proof: Proof. by move=> Aa; apply/setP=> x /[!inE]; case: eqP => // ->. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)