Package list-replicate: Definitions and theorems about the list replicate function

Information

namelist-replicate
version1.11
description Definitions and theorems about the list replicate function
authorJoe Hurd <joe@gilith.com>
licenseMIT
showData.Bool
Data.List
Number.Natural

Files

Defined Constant

Theorems

n x. length (replicate n x) = n

n x i. i < n nth i (replicate n x) = x

n x. toSet (replicate n x) = if n = 0 then Set.∅ else Set.insert x Set.∅

(x. replicate 0 x = []) x n. replicate (suc n) x = x :: replicate n x

Input Type Operators

Input Constants

Assumptions

T

F p. p

(~) = λp. p F

() = λP. P ((select) P)

t. (x. t) t

() = λp. p = λx. T

x. x = x T

n. ¬(suc n = 0)

() = λp q. p q p

h t. nth 0 (h :: t) = h

m. m = 0 n. m = suc n

() = λp q. (λf. f p q) = λf. f T T

() = λP. q. (x. P x q) q

x s. Set.insert x (Set.insert x s) = Set.insert x s

m n. suc m < suc n m < n

() = λp q. r. (p r) (q r) r

t1 t2. (if T then t1 else t2) = t1 (if F then t1 else t2) = t2

length [] = 0 h t. length (h :: t) = suc (length t)

P. P 0 (n. P n P (suc n)) n. P n

toSet [] = Set.∅ h t. toSet (h :: t) = Set.insert h (toSet t)

e f. fn. fn 0 = e n. fn (suc n) = f (fn n) n

h t n. n < length t nth (suc n) (h :: t) = nth n t

P c x y. P (if c then x else y) (c P x) (¬c P y)

(m. m < 0 F) m n. m < suc n m = n m < n

t. (T t t) (t T T) (F t T) (t t T) (t F ¬t)