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Add a uniqueness property

This commit is contained in:
Nathan van Doorn 2024-06-22 16:52:06 +02:00
parent d2557b6967
commit 3e2ea54030
1 changed files with 8 additions and 1 deletions
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9
src/Thinning/Triangle.agda
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@ -14,7 +14,7 @@ private
A : Set a A : Set a
x : A x : A
xs ys zs : List A xs ys zs : List A
θ φ ψ : Thinning A xs ys θ φ φ′ ψ : Thinning A xs ys
-- Thinning triangles -- Thinning triangles
------------------------------------------------------------------------ ------------------------------------------------------------------------
@ -46,3 +46,10 @@ untriangle end = refl
untriangle (include ▴) = cong include (untriangle ▴) untriangle (include ▴) = cong include (untriangle ▴)
untriangle (occlude ▴) = cong exclude (untriangle ▴) untriangle (occlude ▴) = cong exclude (untriangle ▴)
untriangle (exclude ▴) = cong exclude (untriangle ▴) untriangle (exclude ▴) = cong exclude (untriangle ▴)
-- If we have two triangles with common edges, the third edge must also be equal
triangleUnique : Triangle A θ φ ψ → Triangle A θ φ′ ψ → φ ≡ φ′
triangleUnique end end = refl
triangleUnique (include ▴) (include ▵) = cong include (triangleUnique ▴ ▵)
triangleUnique (occlude ▴) (occlude ▵) = triangleUnique ▴ ▵
triangleUnique (exclude ▴) (exclude ▵) = cong exclude (triangleUnique ▴ ▵)