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

Lemma comparisonE :
forall v1 v2 : nat, v1 = v2 -> Compare_Nat.comparison v1 v2 = E.