intros.
unfold Compare_Nat.comparison in |- *.
elim (Lt_eq_Gt v1 v2); auto with arith.
intro; absurd (v1 < v2); auto with arith.
rewrite H; auto with arith.
intro; absurd (v1 > v2); auto with arith.
rewrite H; auto with arith.
Qed.
Hint Resolve comparisonE.

Lemma inv_comparisonL :
forall v1 v2 : nat, Compare_Nat.comparison v1 v2 = L -> v1 < v2.