Package list-nth-def: Definition of the list nth function

Information

namelist-nth-def
version1.24
descriptionDefinition of the list nth function
authorJoe Hurd <joe@gilith.com>
licenseHOLLight
provenanceHOL Light theory extracted on 2011-11-27
requiresbool
natural
list-dest
showData.Bool
Data.List
Number.Natural

Files

Defined Constant

Theorems

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

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

Input Type Operators

Input Constants

Assumptions

T

() = λP. P ((select) P)

t. (x. t) t

() = λp. p = λx. T

t. t T T

() = λp q. p q p

h t. head (h :: t) = h

h t. tail (h :: t) = t

() = λp q. (λf. f p q) = λf. f T T

() = λP. q. (x. P x q) q

(∃!) = λP. () P x y. P x P y x = y

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