Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

[Refractor] ⊥-elim to contradiction1 in asym⇒antisym def #2655

Closed
wants to merge 2 commits into from
Closed

[Refractor] ⊥-elim to contradiction1 in asym⇒antisym def #2655

Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
bef7264
[Refractor] ⊥-elim to contradiction1 in asym⇒antisym def
jmougeot Mar 12, 2025
62a09e8
fix-whitespace
jmougeot Mar 12, 2025
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
4 changes: 2 additions & 2 deletions src/Relation/Binary/Consequences.agda
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -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)
Expand Down Expand Up @@ -121,7 +121,7 @@ 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 _≈_ _<_
Expand Down