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Fill in missing Nat proofs

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This commit is contained in:
Nick Drozd 2020-06-11 17:06:05 -05:00
parent 3b0496b8ab
commit b096062858
1 changed files with 18 additions and 18 deletions
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36
libs/base/Data/Nat.idr
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@ -519,9 +519,9 @@ maximumCommutative Z (S _) = Refl
maximumCommutative (S _) Z = Refl maximumCommutative (S _) Z = Refl
maximumCommutative (S k) (S j) = rewrite maximumCommutative k j in Refl maximumCommutative (S k) (S j) = rewrite maximumCommutative k j in Refl
-- maximumIdempotent : (n : Nat) -> maximum n n = n maximumIdempotent : (n : Nat) -> maximum n n = n
-- maximumIdempotent Z = Refl maximumIdempotent Z = Refl
-- maximumIdempotent (S k) = cong $ maximumIdempotent k maximumIdempotent (S k) = cong S $ maximumIdempotent k
minimumAssociative : (l, c, r : Nat) -> minimumAssociative : (l, c, r : Nat) ->
minimum l (minimum c r) = minimum (minimum l c) r minimum l (minimum c r) = minimum (minimum l c) r
@ -536,9 +536,9 @@ minimumCommutative Z (S _) = Refl
minimumCommutative (S _) Z = Refl minimumCommutative (S _) Z = Refl
minimumCommutative (S k) (S j) = rewrite minimumCommutative k j in Refl minimumCommutative (S k) (S j) = rewrite minimumCommutative k j in Refl
-- minimumIdempotent : (n : Nat) -> minimum n n = n minimumIdempotent : (n : Nat) -> minimum n n = n
-- minimumIdempotent Z = Refl minimumIdempotent Z = Refl
-- minimumIdempotent (S k) = cong (minimumIdempotent k) minimumIdempotent (S k) = cong S $ minimumIdempotent k
minimumZeroZeroLeft : (left : Nat) -> minimum left 0 = Z minimumZeroZeroLeft : (left : Nat) -> minimum left 0 = Z
minimumZeroZeroLeft left = rewrite minimumCommutative left 0 in Refl minimumZeroZeroLeft left = rewrite minimumCommutative left 0 in Refl
@ -554,18 +554,18 @@ maximumSuccSucc : (left, right : Nat) ->
S (maximum left right) = maximum (S left) (S right) S (maximum left right) = maximum (S left) (S right)
maximumSuccSucc _ _ = Refl maximumSuccSucc _ _ = Refl
-- sucMaxL : (l : Nat) -> maximum (S l) l = (S l) sucMaxL : (l : Nat) -> maximum (S l) l = (S l)
-- sucMaxL Z = Refl sucMaxL Z = Refl
-- sucMaxL (S l) = cong $ sucMaxL l sucMaxL (S l) = cong S $ sucMaxL l
-- sucMaxR : (l : Nat) -> maximum l (S l) = (S l) sucMaxR : (l : Nat) -> maximum l (S l) = (S l)
-- sucMaxR Z = Refl sucMaxR Z = Refl
-- sucMaxR (S l) = cong $ sucMaxR l sucMaxR (S l) = cong S $ sucMaxR l
-- sucMinL : (l : Nat) -> minimum (S l) l = l sucMinL : (l : Nat) -> minimum (S l) l = l
-- sucMinL Z = Refl sucMinL Z = Refl
-- sucMinL (S l) = cong $ sucMinL l sucMinL (S l) = cong S $ sucMinL l
-- sucMinR : (l : Nat) -> minimum l (S l) = l sucMinR : (l : Nat) -> minimum l (S l) = l
-- sucMinR Z = Refl sucMinR Z = Refl
-- sucMinR (S l) = cong $ sucMinR l sucMinR (S l) = cong S $ sucMinR l