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] contradiction over ⊥-elim in trans∧tri⇒respʳ & trans∧tri⇒respˡ def #2657

Merged
merged 3 commits into from
Mar 14, 2025
Merged

[Refractor] contradiction over ⊥-elim in trans∧tri⇒respʳ & trans∧tri⇒respˡ def #2657

Changes from 2 commits
Commits
Show all changes
3 commits
Select commit Hold shift + click to select a range
88b84ed
[Refractor] contradiction over ⊥-elim in trans∧tri⇒respʳ & trans∧tri…
jmougeot Mar 12, 2025
0174dac
[Refractor] contradiction over ⊥-elim in trans∧tri⇒respʳ & trans∧tri…
jmougeot Mar 12, 2025
ad73edd
contradiction over bot/elim
jmougeot Mar 13, 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
10 changes: 5 additions & 5 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 @@ -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 _≈_ _<_ →
Expand Down