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Manual
haskell.org
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author:Ãmer-Sinan-AÄacan
author:ÐÑигоÑий-ХоломÑÑв
succ package:type-natural
pattern
Succ
:: forall n . () => forall n1 . n ~ Succ n1 => SNat n1 -> SNat n
type-natural
Data.Type.Natural
type
Succ
n = n + 1
type-natural
Data.Type.Natural
Data.Type.Natural.Lemma.Arithmetic
pattern
Succ
:: forall n n1 . () => n ~ Succ n1 => SNat n1 -> SNat n
type-natural
Data.Type.Natural.Lemma.Arithmetic
succ
AndPlusOneL
:: SNat n -> Succ n :~: (1 + n)
type-natural
Data.Type.Natural.Lemma.Arithmetic
succ
AndPlusOneR
:: SNat n -> Succ n :~: (n + 1)
type-natural
Data.Type.Natural.Lemma.Arithmetic
succ
Cong
:: (n :~: m) -> S n :~: S m
type-natural
Data.Type.Natural.Lemma.Arithmetic
succ
Inj
:: (Succ n :~: Succ m) -> n :~: m
type-natural
Data.Type.Natural.Lemma.Arithmetic
succ
Inj'
:: proxy n -> proxy' m -> (Succ n :~: Succ m) -> n :~: m
type-natural
Data.Type.Natural.Lemma.Arithmetic
succ
NonCyclic
:: SNat n -> (Succ n :~: 0) -> Void
type-natural
Data.Type.Natural.Lemma.Arithmetic
succ
OneCong
:: Succ 0 :~: 1
type-natural
Data.Type.Natural.Lemma.Arithmetic
succ
Pred
:: SNat n -> ((n :~: 0) -> Void) -> Succ (Pred n) :~: n
type-natural
Data.Type.Natural.Lemma.Arithmetic
succ
DiffNat
:: SNat n -> SNat m -> DiffNat n m -> DiffNat (Succ n) (Succ m)
type-natural
Data.Type.Natural.Lemma.Order
succ
LeqAbsurd
:: SNat n -> IsTrue (S n <=? n) -> Void
type-natural
Data.Type.Natural.Lemma.Order
succ
LeqAbsurd'
:: SNat n -> (S n <=? n) :~: 'False
type-natural
Data.Type.Natural.Lemma.Order
succ
LeqToLT
:: SNat a -> SNat b -> IsTrue (S a <=? b) -> CmpNat a b :~: 'LT
type-natural
Data.Type.Natural.Lemma.Order
succ
LeqZeroAbsurd
:: SNat n -> IsTrue (S n <=? 0) -> Void
type-natural
Data.Type.Natural.Lemma.Order
succ
LeqZeroAbsurd'
:: SNat n -> (S n <=? 0) :~: 'False
type-natural
Data.Type.Natural.Lemma.Order
succ
Lneq
Succ
:: SNat n -> SNat m -> (n <? m) :~: (Succ n <? Succ m)
type-natural
Data.Type.Natural.Lemma.Order
Succ
Leq
Succ
:: Leq n m -> Leq (n + 1) (m + 1)
type-natural
Data.Type.Natural.Lemma.Order
Is
Succ
:: SNat n -> ZeroOrSucc (n + 1)
type-natural
Data.Type.Natural
Data.Type.Natural.Lemma.Arithmetic
data
ZeroOr
Succ
n
type-natural
Data.Type.Natural
Data.Type.Natural.Lemma.Arithmetic
s
Succ
:: SNat n -> SNat (Succ n)
type-natural
Data.Type.Natural
zeroOr
Succ
:: SNat n -> ZeroOrSucc n
type-natural
Data.Type.Natural
multEq
Succ
ElimL
:: SNat n -> SNat m -> SNat l -> ((n * m) :~: Succ l) -> n :~: Succ (Pred n)
type-natural
Data.Type.Natural.Lemma.Arithmetic
multEq
Succ
ElimR
:: SNat n -> SNat m -> SNat l -> ((n * m) :~: Succ l) -> m :~: Succ (Pred m)
type-natural
Data.Type.Natural.Lemma.Arithmetic