Section BasicLemmas.
Variable X Y: Type.
Implicit Type f: X -> Y.
Implicit Type p: X -> bool.
Implicit Type A B C : list X.
Implicit Type a b c : X.
Global Instance proper_in_incl: Proper (eq ++> incl ==> Basics.impl) (@In X).
Global Instance in_seteq_proper: Proper (eq ++> seteq ++> iff) (@In X).
(* ⊆ *)
Global Instance subrel_incl_seteq: subrelation seteq (@incl X).

Lemma wf_strict_incl: well_founded (@strict_incl X).