Definition eq_dec : forall x y, { eq x y } + { ~ eq x y }.Definition t := t.Definition compare := compare.Infix "?=" := compare (at level 70, no associativity).

(* Specifications: *)
Lemma compare_sym : forall x y, (y?=x) = CompOpp (x?=y).
Lemma compare_Eq : forall x y, compare x y = Eq <-> eq x y.
Lemma compare_Lt : forall x y, compare x y = Lt <-> lt x y.
Lemma compare_Gt : forall x y, compare x y = Gt <-> lt y x.
Lemma compare_trans : forall c x y z, (x?=y) = c -> (y?=z) = c -> (x?=z) = c.