Load loadpath.
Definition StrictCompSpec {A} (eq lt: A -> A -> Prop)
(cmp: A -> A -> comparison) :=
StrictOrder lt /\ forall x y, CompSpec eq lt x y (cmp x y).
Definition CompSpec' {A} (cmp: A -> A -> comparison) :=
StrictCompSpec (@Logic.eq A) (fun x y => Lt = cmp x y) cmp.
Ltac do_comp cspec x y := destruct (CompSpec2Type (proj2 cspec x y)).

Lemma eq_comp: forall {A} lt cmp,
StrictCompSpec Logic.eq lt cmp ->
forall x y: A,   (x = y <-> Eq = cmp x y).