intros v1 v2 c.
elim (Lt_eq_Gt v1 v2); auto with arith.
intros l; absurd (Compare_Nat.comparison v1 v2 = E); auto with arith.
rewrite (comparisonL v1 v2 l); discriminate.
intros g; absurd (Compare_Nat.comparison v1 v2 = E); auto with arith.
rewrite (comparisonG v1 v2 g); discriminate.
Qed.
Hint Resolve inv_comparisonE.

(* Specifications: *)
Lemma inv_comparisonG :
forall v1 v2 : nat, Compare_Nat.comparison v1 v2 = G -> v1 > v2.