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[Refractor] contradiction over ⊥-elim in ×-antisymmetric def #2662

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Merged
jamesmckinna merged 3 commits into from
Mar 14, 2025
Merged

[Refractor] contradiction over ⊥-elim in ×-antisymmetric def #2662

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12ad5a5
[Refractor] contradiction over ⊥-elim in ×-antisymmetric def
jmougeot Mar 12, 2025
0c6138e
Update src/Data/Product/Relation/Binary/Lex/Strict.agda
jmougeot Mar 13, 2025
9f0cb9b
Update src/Data/Product/Relation/Binary/Lex/Strict.agda
JacquesCarette Mar 13, 2025
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7 changes: 4 additions & 3 deletions src/Data/Product/Relation/Binary/Lex/NonStrict.agda
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Original file line number Diff line number Diff line change
Expand Up @@ -12,6 +12,9 @@
module Data.Product.Relation.Binary.Lex.NonStrict where

open import Data.Product.Base using (_×_; _,_; proj₁; proj₂)
open import Data.Product.Relation.Binary.Pointwise.NonDependent as Pointwise
using (Pointwise)
import Data.Product.Relation.Binary.Lex.Strict as Strict
open import Data.Sum.Base using (inj₁; inj₂)
open import Level using (Level)
open import Relation.Binary.Core using (Rel; _⇒_)
Expand All @@ -24,9 +27,7 @@ open import Relation.Binary.Definitions
; Irreflexive; Asymmetric; _Respects₂_; tri<; tri>; tri≈)
open import Relation.Binary.Consequences
import Relation.Binary.Construct.NonStrictToStrict as Conv
open import Data.Product.Relation.Binary.Pointwise.NonDependent as Pointwise
using (Pointwise)
import Data.Product.Relation.Binary.Lex.Strict as Strict


private
variable
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10 changes: 5 additions & 5 deletions src/Data/Product/Relation/Binary/Lex/Strict.agda
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Expand Up @@ -15,11 +15,9 @@ open import Data.Product.Base
open import Data.Product.Relation.Binary.Pointwise.NonDependent as Pointwise
using (Pointwise)
open import Data.Sum.Base using (inj₁; inj₂; _-⊎-_; [_,_])
open import Data.Empty using (⊥-elim)
open import Function.Base using (flip; _on_; _$_; _∘_)
open import Induction.WellFounded using (Acc; acc; WfRec; WellFounded; Acc-resp-flip-≈)
open import Level using (Level)
open import Relation.Nullary.Decidable using (yes; no; _⊎-dec_; _×-dec_)
open import Relation.Binary.Core using (Rel; _⇒_)
open import Relation.Binary.Bundles
using (Preorder; StrictPartialOrder; StrictTotalOrder)
Expand All @@ -31,6 +29,8 @@ open import Relation.Binary.Definitions
; tri<; tri>; tri≈)
open import Relation.Binary.Consequences using (asym⇒irr)
open import Relation.Binary.PropositionalEquality.Core as ≡ using (_≡_)
open import Relation.Nullary.Decidable.Core using (yes; no; _⊎-dec_; _×-dec_)
open import Relation.Nullary.Negation.Core using (contradiction)

private
variable
Expand Down Expand Up @@ -134,11 +134,11 @@ module _ {_≈₁_ : Rel A ℓ₁} {_<₁_ : Rel A ℓ₂}
where
antisym : Antisymmetric _≋_ _<ₗₑₓ_
antisym (inj₁ x₁<y₁) (inj₁ y₁<x₁) =
⊥-elim $ asym₁ x₁<y₁ y₁<x₁
contradiction y₁<x₁ (asym₁ x₁<y₁)
antisym (inj₁ x₁<y₁) (inj₂ y≈≤x) =
⊥-elim $ irrefl₁ (sym₁ $ proj₁ y≈≤x) x₁<y₁
contradiction x₁<y₁ (irrefl₁ (sym₁ $ proj₁ y≈≤x))
antisym (inj₂ x≈≤y) (inj₁ y₁<x₁) =
⊥-elim $ irrefl₁ (sym₁ $ proj₁ x≈≤y) y₁<x₁
contradiction y₁<x₁ (irrefl₁ (sym₁ $ proj₁ x≈≤y))
antisym (inj₂ x≈≤y) (inj₂ y≈≤x) =
proj₁ x≈≤y , antisym₂ (proj₂ x≈≤y) (proj₂ y≈≤x)

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