Instance find_elt_compat A dom (m : t A dom) : Proper (X.eq ==> Logic.eq) (fun x => find x m).

Lemma constant_aux : forall A v x u l (m : S.t A), NoDupA X.eq l -> S.find x (fold_left (fun a e => S.add e v a) l m) = Some u <-> InA X.eq x l ∧ u = v ∨ ¬InA X.eq x l ∧ S.find x m = Some u.