proposition: Lemma Zcompare_Gt_Lt_antisym : forall n m:Z, (n ?= m) = Gt <-> (m ?= n) = Lt.
proof: Proof. Proof Z.gt_lt_iff. Lemma Zcompare_antisym n m : CompOpp (n ?= m) = (m ?= n). Proof eq_sym (Z.compare_antisym n m). Lemma Zcompare_Lt_trans : forall n m p:Z, (n ?= m) = Lt -> (m ?= p) = Lt -> (n ?= p) = Lt. Proof Z.lt_trans. Lemma Zcompare_Gt_trans : forall n m p:Z, (n ?= m) = Gt -> (m ?= p) = Gt -> (n ?= p) = Gt. Proof. intros n m p. change (n > m -> m > p -> n > p). Z.swap_greater. intros. now transitivity m. Qed.
imports: BinPos BinInt