intros v1 v2.
cut (Compare_Nat.comparison v1 v2 = Compare_Nat.comparison v1 v2);
auto with arith.
pattern (Compare_Nat.comparison v1 v2) at 2 3 in |- *.
case (Compare_Nat.comparison v1 v2); intro; auto with arith.
Qed.

Lemma comp_sym_LG :
forall v1 v2 : nat,
Compare_Nat.comparison v1 v2 = L -> Compare_Nat.comparison v2 v1 = G.