From e5b43dcd5f449ccbc84c32868f9a9f6c3b73b263 Mon Sep 17 00:00:00 2001 From: Raphaël Monat Date: Thu, 12 Oct 2017 13:45:19 +0200 Subject: Added proofs of Qeq_bool_refl, Qeq_bool_sym, Qeq_bool_trans. --- theories/QArith/QArith_base.v | 15 +++++++++++++++ 1 file changed, 15 insertions(+) (limited to 'theories') diff --git a/theories/QArith/QArith_base.v b/theories/QArith/QArith_base.v index a94435c3f..121527c63 100644 --- a/theories/QArith/QArith_base.v +++ b/theories/QArith/QArith_base.v @@ -176,6 +176,21 @@ Proof. apply eq_true_iff_eq. rewrite !Qeq_bool_iff. now symmetry. Qed. +Lemma Qeq_bool_refl x: is_true (Qeq_bool x x). +Proof. + unfold is_true. rewrite Qeq_bool_iff. now reflexivity. +Qed. + +Lemma Qeq_bool_sym x y: is_true (Qeq_bool x y) -> is_true (Qeq_bool y x). +Proof. + unfold is_true. rewrite !Qeq_bool_iff. now symmetry. +Qed. + +Lemma Qeq_bool_trans x y z: is_true (Qeq_bool x y) -> is_true (Qeq_bool y z) -> is_true (Qeq_bool x z). +Proof. + unfold is_true. rewrite !Qeq_bool_iff. apply Qeq_trans. +Qed. + Hint Resolve Qnot_eq_sym : qarith. (** * Addition, multiplication and opposite *) -- cgit v1.2.3