Global Instance InfA_compat : Proper (eqA==>eqlistA==>iff) InfA.

(* Specifications: *)
Lemma InfA_eqA l x y : eqA x y -> InfA y l -> InfA x l.
Lemma SortA_InfA_InA : forall l x a, SortA l -> InfA a l -> InA x l -> ltA a x.
Lemma In_InfA : forall l x, (forall y, In y l -> ltA x y) -> InfA x l.
Lemma InA_InfA : forall l x, (forall y, InA y l -> ltA x y) -> InfA x l.
Lemma InfA_alt : forall l x, SortA l -> (InfA x l <-> (forall y, InA y l -> ltA x y)).
Lemma InfA_app : forall l1 l2 a, InfA a l1 -> InfA a l2 -> InfA a (l1++l2).
Lemma SortA_app : forall l1 l2, SortA l1 -> SortA l2 -> (forall x y, InA x l1 -> InA y l2 -> ltA x y) -> SortA (l1 ++ l2).
Lemma SortA_NoDupA : forall l, SortA l -> NoDupA l.
Lemma eqlistA_length : forall l l', eqlistA l l' -> length l = length l'.