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Move factorial from Cubical.Data.Fin.LehmerCode to Cubical.Data.Nat.Properties #1184

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Merged
felixwellen merged 7 commits into from
Feb 14, 2025
Merged

Move factorial from Cubical.Data.Fin.LehmerCode to Cubical.Data.Nat.Properties #1184

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24f4632
Update LehmerCode.agda
anshwad10 Feb 9, 2025
2696726
Update Properties.agda
anshwad10 Feb 9, 2025
fdadeb5
Update LehmerCode.agda
anshwad10 Feb 9, 2025
b25b61d
Removed dependency on LehmerCode exporting `factorial`
anshwad10 Feb 14, 2025
2772cc1
Removed dependency on LehmerCode exporting `factorial`
anshwad10 Feb 14, 2025
630f3be
Removed dependency on LehmerCode exporting `factorial`
anshwad10 Feb 14, 2025
b9386f3
Remove the public export of `factorial` from LehmerCode.agda
anshwad10 Feb 14, 2025
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4 changes: 0 additions & 4 deletions Cubical/Data/Fin/LehmerCode.agda
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Expand Up @@ -191,10 +191,6 @@ encode = equivFun lehmerEquiv
decode : LehmerCode n → Fin n ≃ Fin n
decode = invEq lehmerEquiv

-- Use the one in Cubical.Data.Nat.Properties instead
factorial : ℕ → ℕ
factorial = _!

lehmerFinEquiv : LehmerCode n ≃ Fin (n !)
lehmerFinEquiv {zero} = isContr→Equiv isContrLehmerZero isContrFin1
lehmerFinEquiv {suc n} = _ ≃⟨ invEquiv lehmerSucEquiv ⟩
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2 changes: 1 addition & 1 deletion Cubical/Data/FinSet/Cardinality.agda
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Expand Up @@ -379,7 +379,7 @@ module _
module _
(X : FinSet ℓ ) where

cardAut : card (_ , isFinSetAut X) ≡ LehmerCode.factorial (card X)
cardAut : card (_ , isFinSetAut X) ≡ (card X !)
cardAut = refl

module _
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2 changes: 1 addition & 1 deletion Cubical/Data/FinSet/Constructors.agda
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Expand Up @@ -168,7 +168,7 @@ module _
(X : FinSet ℓ) where

isFinSetAut : isFinSet (X .fst ≃ X .fst)
isFinSetAut = LehmerCode.factorial (card X) ,
isFinSetAut = card X ! ,
Prop.map (λ p → isFinOrd≃ (X .fst) (card X , p) .snd) (X .snd .snd)

isFinSetTypeAut : isFinSet (X .fst ≡ X .fst)
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8 changes: 5 additions & 3 deletions Cubical/Data/Nat/Properties.agda
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Expand Up @@ -266,12 +266,14 @@ n∸n (suc n) = n∸n n
∸-distribʳ zero (suc n) k = sym (zero∸ (k + n · k))
∸-distribʳ (suc m) (suc n) k = ∸-distribʳ m n k ∙ sym (∸-cancelˡ k (m · k) (n · k))


infix 6 _!
infix 7 _choose_

-- factorial:
_! : ℕ → ℕ
_! factorial : ℕ → ℕ
zero ! = 1
suc n ! = (suc n) · (n !)
suc n ! = suc n · (n !)
factorial = _!

--binomial coefficient:
_choose_ : ℕ → ℕ → ℕ
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2 changes: 1 addition & 1 deletion Cubical/Data/SumFin/Properties.agda
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Expand Up @@ -264,7 +264,7 @@ isProp→Fin≤1 (suc (suc n)) p = ⊥.rec (fzero≠fone (p fzero (fsuc fzero)))

-- automorphisms of SumFin

SumFin≃≃ : (n : ℕ) → (Fin n ≃ Fin n) ≃ Fin (LehmerCode.factorial n)
SumFin≃≃ : (n : ℕ) → (Fin n ≃ Fin n) ≃ Fin (n !)
SumFin≃≃ _ =
equivComp (SumFin≃Fin _) (SumFin≃Fin _)
⋆ LehmerCode.lehmerEquiv
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