End ForNotations.
Definition In := InA X.eq.
#[global]
Instance In_compat : Proper (X.eq==>eq==> iff) In.
#[global]
Instance lt_compat : Proper (eq==>eq==>iff) lt.

(* Specifications: *)
Lemma compare_spec_aux : forall s s', CompSpec eq L.lt s s' (compare s s').
Lemma compare_spec : forall s s', Ok s -> Ok s' ->
CompSpec eq lt s s' (compare s s').