From 88b84eddaed686b982f4027727d03021e242450e Mon Sep 17 00:00:00 2001 From: Jacques <jacques.mougeot@centrale-med.fr> Date: Wed, 12 Mar 2025 15:00:45 -0400 Subject: [PATCH 1/3] =?UTF-8?q?=20[Refractor]=20contradiction=20over=20?= =?UTF-8?q?=E2=8A=A5-elim=20in=20trans=E2=88=A7tri=E2=87=92resp=CA=B3=20&?= =?UTF-8?q?=20trans=E2=88=A7tri=E2=87=92resp=CB=A1=20def?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/Relation/Binary/Consequences.agda | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/src/Relation/Binary/Consequences.agda b/src/Relation/Binary/Consequences.agda index 3cdb4db356..4b3d3927d3 100644 --- a/src/Relation/Binary/Consequences.agda +++ b/src/Relation/Binary/Consequences.agda @@ -15,7 +15,7 @@ open import Function.Base using (_∘_; _∘₂_; _$_; flip) open import Level using (Level) open import Relation.Binary.Core open import Relation.Binary.Definitions -open import Relation.Nullary.Negation.Core using (¬_) +open import Relation.Nullary.Negation.Core using (¬_; contradiction) open import Relation.Nullary.Decidable.Core using (yes; no; recompute; map′; dec⇒maybe) open import Relation.Unary using (∁; Pred) @@ -157,16 +157,16 @@ module _ {_≈_ : Rel A ℓ₁} {_<_ : Rel A ℓ₂} where _<_ Respectsʳ _≈_ trans∧tri⇒respʳ sym ≈-tr <-tr tri {x} {y} {z} y≈z x<y with tri x z ... | tri< x<z _ _ = x<z - ... | tri≈ _ x≈z _ = ⊥-elim (tri⇒irr tri (≈-tr x≈z (sym y≈z)) x<y) - ... | tri> _ _ z<x = ⊥-elim (tri⇒irr tri (sym y≈z) (<-tr z<x x<y)) + ... | tri≈ _ x≈z _ = contradiction x<y (tri⇒irr tri (≈-tr x≈z (sym y≈z))) + ... | tri> _ _ z<x = contradiction (<-tr z<x x<y) (tri⇒irr tri (sym y≈z)) trans∧tri⇒respˡ : Transitive _≈_ → Transitive _<_ → Trichotomous _≈_ _<_ → _<_ Respectsˡ _≈_ trans∧tri⇒respˡ ≈-tr <-tr tri {z} {_} {y} x≈y x<z with tri y z ... | tri< y<z _ _ = y<z - ... | tri≈ _ y≈z _ = ⊥-elim (tri⇒irr tri (≈-tr x≈y y≈z) x<z) - ... | tri> _ _ z<y = ⊥-elim (tri⇒irr tri x≈y (<-tr x<z z<y)) + ... | tri≈ _ y≈z _ = contradiction x<z (tri⇒irr tri (≈-tr x≈y y≈z)) + ... | tri> _ _ z<y = contradiction (<-tr x<z z<y) (tri⇒irr tri x≈y) trans∧tri⇒resp : Symmetric _≈_ → Transitive _≈_ → Transitive _<_ → Trichotomous _≈_ _<_ → From 0174dacec3dc1992d76565962534c856fb032b69 Mon Sep 17 00:00:00 2001 From: Jacques <jacques.mougeot@centrale-med.fr> Date: Wed, 12 Mar 2025 15:01:39 -0400 Subject: [PATCH 2/3] =?UTF-8?q?=20[Refractor]=20contradiction=20over=20?= =?UTF-8?q?=E2=8A=A5-elim=20in=20trans=E2=88=A7tri=E2=87=92resp=CA=B3=20&?= =?UTF-8?q?=20trans=E2=88=A7tri=E2=87=92resp=CB=A1=20def?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/Relation/Binary/Consequences.agda | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Relation/Binary/Consequences.agda b/src/Relation/Binary/Consequences.agda index 4b3d3927d3..424b48e451 100644 --- a/src/Relation/Binary/Consequences.agda +++ b/src/Relation/Binary/Consequences.agda @@ -158,7 +158,7 @@ module _ {_≈_ : Rel A ℓ₁} {_<_ : Rel A ℓ₂} where trans∧tri⇒respʳ sym ≈-tr <-tr tri {x} {y} {z} y≈z x<y with tri x z ... | tri< x<z _ _ = x<z ... | tri≈ _ x≈z _ = contradiction x<y (tri⇒irr tri (≈-tr x≈z (sym y≈z))) - ... | tri> _ _ z<x = contradiction (<-tr z<x x<y) (tri⇒irr tri (sym y≈z)) + ... | tri> _ _ z<x = contradiction (<-tr z<x x<y) (tri⇒irr tri (sym y≈z)) trans∧tri⇒respˡ : Transitive _≈_ → Transitive _<_ → Trichotomous _≈_ _<_ → From ad73edd019aed919963e35137330423e4141f83a Mon Sep 17 00:00:00 2001 From: Jacques <jacques.mougeot@centrale-med.fr> Date: Thu, 13 Mar 2025 14:34:53 -0400 Subject: [PATCH 3/3] contradiction over bot/elim --- src/Relation/Binary/Consequences.agda | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/src/Relation/Binary/Consequences.agda b/src/Relation/Binary/Consequences.agda index 424b48e451..9add6af3a0 100644 --- a/src/Relation/Binary/Consequences.agda +++ b/src/Relation/Binary/Consequences.agda @@ -8,7 +8,6 @@ module Relation.Binary.Consequences where -open import Data.Empty using (⊥-elim) open import Data.Product.Base using (_,_) open import Data.Sum.Base as Sum using (inj₁; inj₂; [_,_]′) open import Function.Base using (_∘_; _∘₂_; _$_; flip) @@ -121,7 +120,7 @@ module _ {_≈_ : Rel A ℓ₁} {_<_ : Rel A ℓ₂} where irrefl (antisym x<y y<x) x<y asym⇒antisym : Asymmetric _<_ → Antisymmetric _≈_ _<_ - asym⇒antisym asym x<y y<x = ⊥-elim (asym x<y y<x) + asym⇒antisym asym x<y y<x = contradiction y<x (asym x<y) asym⇒irr : _<_ Respects₂ _≈_ → Symmetric _≈_ → Asymmetric _<_ → Irreflexive _≈_ _<_