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Data.Nat proofs should be exported

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I assumed these were copied directly from the Idris 1 libraries, where
there was an %access directive that we don't have any more.
This commit is contained in:
Edwin Brady 2020-07-10 22:59:46 +01:00
parent 9156084075
commit 58e28170ac
1 changed files with 14 additions and 0 deletions
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14
libs/base/Data/Nat.idr
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@ -506,6 +506,7 @@ multDistributesOverMinusRight left centre right =
-- minimum / maximum proofs
export
maximumAssociative : (l, c, r : Nat) ->
maximum l (maximum c r) = maximum (maximum l c) r
maximumAssociative Z _ _ = Refl
@ -513,16 +514,19 @@ maximumAssociative (S _) Z _ = Refl
maximumAssociative (S _) (S _) Z = Refl
maximumAssociative (S k) (S j) (S i) = rewrite maximumAssociative k j i in Refl
export
maximumCommutative : (l, r : Nat) -> maximum l r = maximum r l
maximumCommutative Z Z = Refl
maximumCommutative Z (S _) = Refl
maximumCommutative (S _) Z = Refl
maximumCommutative (S k) (S j) = rewrite maximumCommutative k j in Refl
export
maximumIdempotent : (n : Nat) -> maximum n n = n
maximumIdempotent Z = Refl
maximumIdempotent (S k) = cong S $ maximumIdempotent k
export
minimumAssociative : (l, c, r : Nat) ->
minimum l (minimum c r) = minimum (minimum l c) r
minimumAssociative Z _ _ = Refl
@ -530,42 +534,52 @@ minimumAssociative (S _) Z _ = Refl
minimumAssociative (S _) (S _) Z = Refl
minimumAssociative (S k) (S j) (S i) = rewrite minimumAssociative k j i in Refl
export
minimumCommutative : (l, r : Nat) -> minimum l r = minimum r l
minimumCommutative Z Z = Refl
minimumCommutative Z (S _) = Refl
minimumCommutative (S _) Z = Refl
minimumCommutative (S k) (S j) = rewrite minimumCommutative k j in Refl
export
minimumIdempotent : (n : Nat) -> minimum n n = n
minimumIdempotent Z = Refl
minimumIdempotent (S k) = cong S $ minimumIdempotent k
export
minimumZeroZeroLeft : (left : Nat) -> minimum left 0 = Z
minimumZeroZeroLeft left = rewrite minimumCommutative left 0 in Refl
export
minimumSuccSucc : (left, right : Nat) ->
minimum (S left) (S right) = S (minimum left right)
minimumSuccSucc _ _ = Refl
export
maximumZeroNLeft : (left : Nat) -> maximum left Z = left
maximumZeroNLeft left = rewrite maximumCommutative left Z in Refl
export
maximumSuccSucc : (left, right : Nat) ->
S (maximum left right) = maximum (S left) (S right)
maximumSuccSucc _ _ = Refl
export
sucMaxL : (l : Nat) -> maximum (S l) l = (S l)
sucMaxL Z = Refl
sucMaxL (S l) = cong S $ sucMaxL l
export
sucMaxR : (l : Nat) -> maximum l (S l) = (S l)
sucMaxR Z = Refl
sucMaxR (S l) = cong S $ sucMaxR l
export
sucMinL : (l : Nat) -> minimum (S l) l = l
sucMinL Z = Refl
sucMinL (S l) = cong S $ sucMinL l
export
sucMinR : (l : Nat) -> minimum l (S l) = l
sucMinR Z = Refl
sucMinR (S l) = cong S $ sucMinR l