Package list-interval-thm: Properties of the list interval function

Information

namelist-interval-thm
version1.26
descriptionProperties of the list interval function
authorJoe Hurd <joe@gilith.com>
licenseMIT
provenanceHOL Light theory extracted on 2011-11-27
requiresbool
natural
list-length
list-nth
list-interval-def
showData.Bool
Data.List
Number.Natural

Files

Theorems

m n. length (interval m n) = n

m n i. i < n nth i (interval m n) = m + i

Input Type Operators

Input Constants

Assumptions

T

length [] = 0

t. (x. t) t

() = λp. p = λx. T

t. T t t

t. F t T

t. T t t

t. t T T

m. m < 0 F

m. m + 0 = m

m. interval m 0 = []

() = λp q. p q p

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

h t. length (h :: t) = suc (length t)

m. m = 0 n. m = suc n

() = λp q. (λf. f p q) = λf. f T T

() = λP. q. (x. P x q) q

m n. m + suc n = suc (m + n)

m n. suc m + n = suc (m + n)

m n. suc m = suc n m = n

m n. suc m < suc n m < n

() = λp q. r. (p r) (q r) r

m n. interval m (suc n) = m :: interval (suc m) n

P. (x y. P x y) y x. P x y

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

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