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punchOut preserves ordering #1913

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Merged
merged 3 commits into from
Feb 20, 2023
Merged

punchOut preserves ordering #1913

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a54d331
punchOut preserves ordering
Taneb Jan 24, 2023
30c5af6
Add the corresponding properties for punchIn too
Taneb Jan 24, 2023
65f60d1
Name fewer pattern matches and name them better
Taneb Jan 24, 2023
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5 changes: 5 additions & 0 deletions CHANGELOG.md
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Expand Up @@ -1790,6 +1790,11 @@ Other minor changes

ℕ-ℕ≡toℕ‿ℕ- : n ℕ-ℕ i ≡ toℕ (n ℕ- i)

punchIn-mono-≤ : ∀ i (j k : Fin n) → j ≤ k → punchIn i j ≤ punchIn i k
punchIn-cancel-≤ : ∀ i (j k : Fin n) → punchIn i j ≤ punchIn i k → j ≤ k
punchOut-mono-≤ : (i≢j : i ≢ j) (i≢k : i ≢ k) → j ≤ k → punchOut i≢j ≤ punchOut i≢k
punchOut-cancel-≤ : (i≢j : i ≢ j) (i≢k : i ≢ k) → punchOut i≢j ≤ punchOut i≢k → j ≤ k

lower₁-injective : lower₁ i n≢i ≡ lower₁ j n≢j → i ≡ j
pinch-injective : suc i ≢ j → suc i ≢ k → pinch i j ≡ pinch i k → j ≡ k

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26 changes: 26 additions & 0 deletions src/Data/Fin/Properties.agda
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Expand Up @@ -802,6 +802,16 @@ punchIn-injective (suc i) (suc j) (suc k) ↑j+1≡↑k+1 =
punchInᵢ≢i : ∀ i (j : Fin n) → punchIn i j ≢ i
punchInᵢ≢i (suc i) (suc j) = punchInᵢ≢i i j ∘ suc-injective

punchIn-mono-≤ : ∀ i (j k : Fin n) → j ≤ k → punchIn i j ≤ punchIn i k
punchIn-mono-≤ zero _ _ j≤k = s≤s j≤k
punchIn-mono-≤ (suc _) zero _ z≤n = z≤n
punchIn-mono-≤ (suc i) (suc j) (suc k) (s≤s j≤k) = s≤s (punchIn-mono-≤ i j k j≤k)

punchIn-cancel-≤ : ∀ i (j k : Fin n) → punchIn i j ≤ punchIn i k → j ≤ k
punchIn-cancel-≤ zero _ _ (s≤s j≤k) = j≤k
punchIn-cancel-≤ (suc _) zero _ z≤n = z≤n
punchIn-cancel-≤ (suc i) (suc j) (suc k) (s≤s ↑j≤↑k) = s≤s (punchIn-cancel-≤ i j k ↑j≤↑k)

------------------------------------------------------------------------
-- punchOut
------------------------------------------------------------------------
Expand Down Expand Up @@ -835,6 +845,22 @@ punchOut-injective {suc n} {suc i} {zero} {zero} _ _ _ = refl
punchOut-injective {suc n} {suc i} {suc j} {suc k} i≢j i≢k pⱼ≡pₖ =
cong suc (punchOut-injective (i≢j ∘ cong suc) (i≢k ∘ cong suc) (suc-injective pⱼ≡pₖ))

punchOut-mono-≤ : ∀ {i j k : Fin (suc n)} (i≢j : i ≢ j) (i≢k : i ≢ k) →
j ≤ k → punchOut i≢j ≤ punchOut i≢k
punchOut-mono-≤ {_ } {zero } {zero } {_ } 0≢0 _ z≤n = contradiction refl 0≢0
punchOut-mono-≤ {_ } {zero } {suc _} {suc _} _ _ (s≤s j≤k) = j≤k
punchOut-mono-≤ {suc _} {suc _} {zero } {_ } _ _ z≤n = z≤n
punchOut-mono-≤ {suc _} {suc _} {suc _} {suc _} i≢j i≢k (s≤s j≤k) = s≤s (punchOut-mono-≤ (i≢j ∘ cong suc) (i≢k ∘ cong suc) j≤k)

punchOut-cancel-≤ : ∀ {i j k : Fin (suc n)} (i≢j : i ≢ j) (i≢k : i ≢ k) →
punchOut i≢j ≤ punchOut i≢k → j ≤ k
punchOut-cancel-≤ {_ } {zero } {zero } {_ } 0≢0 _ _ = contradiction refl 0≢0
punchOut-cancel-≤ {_ } {zero } {suc _} {zero } _ 0≢0 _ = contradiction refl 0≢0
punchOut-cancel-≤ {suc _} {zero } {suc _} {suc _} _ _ pⱼ≤pₖ = s≤s pⱼ≤pₖ
punchOut-cancel-≤ {_ } {suc _} {zero } {_ } _ _ _ = z≤n
punchOut-cancel-≤ {suc _} {suc _} {suc _} {zero } _ _ ()
punchOut-cancel-≤ {suc _} {suc _} {suc _} {suc _} i≢j i≢k (s≤s pⱼ≤pₖ) = s≤s (punchOut-cancel-≤ (i≢j ∘ cong suc) (i≢k ∘ cong suc) pⱼ≤pₖ)

punchIn-punchOut : ∀ {i j : Fin (suc n)} (i≢j : i ≢ j) →
punchIn i (punchOut i≢j) ≡ j
punchIn-punchOut {_} {zero} {zero} 0≢0 = contradiction refl 0≢0
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