From 62d3e6cbedd2d03579fbe9b76c2cd632c2ac0802 Mon Sep 17 00:00:00 2001 From: Robbert Krebbers <mail@robbertkrebbers.nl> Date: Thu, 16 Jan 2020 09:51:37 +0100 Subject: [PATCH] Replace some occurences of `eq` by `(=)`. --- theories/algebra/big_op.v | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/theories/algebra/big_op.v b/theories/algebra/big_op.v index bed70e68c..d7f86c27d 100644 --- a/theories/algebra/big_op.v +++ b/theories/algebra/big_op.v @@ -132,11 +132,11 @@ Section list. Proof. intros xs1 xs2. apply big_opL_permutation. Qed. Global Instance big_opL_ne n : - Proper (pointwise_relation _ (pointwise_relation _ (dist n)) ==> - eq ==> dist n) (big_opL o (A:=A)). + Proper (pointwise_relation _ (pointwise_relation _ (dist n)) ==> (=) ==> dist n) + (big_opL o (A:=A)). Proof. intros f f' Hf l ? <-. apply big_opL_forall; apply _ || intros; apply Hf. Qed. Global Instance big_opL_proper' : - Proper (pointwise_relation _ (pointwise_relation _ (≡)) ==> eq ==> (≡)) + Proper (pointwise_relation _ (pointwise_relation _ (≡)) ==> (=) ==> (≡)) (big_opL o (A:=A)). Proof. intros f f' Hf l ? <-. apply big_opL_forall; apply _ || intros; apply Hf. Qed. @@ -191,11 +191,11 @@ Section gmap. Proof. apply big_opM_forall; apply _. Qed. Global Instance big_opM_ne n : - Proper (pointwise_relation _ (pointwise_relation _ (dist n)) ==> eq ==> dist n) + Proper (pointwise_relation _ (pointwise_relation _ (dist n)) ==> (=) ==> dist n) (big_opM o (K:=K) (A:=A)). Proof. intros f g Hf m ? <-. apply big_opM_forall; apply _ || intros; apply Hf. Qed. Global Instance big_opM_proper' : - Proper (pointwise_relation _ (pointwise_relation _ (≡)) ==> eq ==> (≡)) + Proper (pointwise_relation _ (pointwise_relation _ (≡)) ==> (=) ==> (≡)) (big_opM o (K:=K) (A:=A)). Proof. intros f g Hf m ? <-. apply big_opM_forall; apply _ || intros; apply Hf. Qed. @@ -297,10 +297,10 @@ Section gset. Proof. apply big_opS_forall; apply _. Qed. Global Instance big_opS_ne n : - Proper (pointwise_relation _ (dist n) ==> eq ==> dist n) (big_opS o (A:=A)). + Proper (pointwise_relation _ (dist n) ==> (=) ==> dist n) (big_opS o (A:=A)). Proof. intros f g Hf m ? <-. apply big_opS_forall; apply _ || intros; apply Hf. Qed. Global Instance big_opS_proper' : - Proper (pointwise_relation _ (≡) ==> eq ==> (≡)) (big_opS o (A:=A)). + Proper (pointwise_relation _ (≡) ==> (=) ==> (≡)) (big_opS o (A:=A)). Proof. intros f g Hf m ? <-. apply big_opS_forall; apply _ || intros; apply Hf. Qed. Lemma big_opS_empty f : ([^o set] x ∈ ∅, f x) = monoid_unit. @@ -384,10 +384,10 @@ Section gmultiset. Proof. apply big_opMS_forall; apply _. Qed. Global Instance big_opMS_ne n : - Proper (pointwise_relation _ (dist n) ==> eq ==> dist n) (big_opMS o (A:=A)). + Proper (pointwise_relation _ (dist n) ==> (=) ==> dist n) (big_opMS o (A:=A)). Proof. intros f g Hf m ? <-. apply big_opMS_forall; apply _ || intros; apply Hf. Qed. Global Instance big_opMS_proper' : - Proper (pointwise_relation _ (≡) ==> eq ==> (≡)) (big_opMS o (A:=A)). + Proper (pointwise_relation _ (≡) ==> (=) ==> (≡)) (big_opMS o (A:=A)). Proof. intros f g Hf m ? <-. apply big_opMS_forall; apply _ || intros; apply Hf. Qed. Lemma big_opMS_empty f : ([^o mset] x ∈ ∅, f x) = monoid_unit. -- GitLab