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

Information

namelist-nth-def
version1.48
descriptionDefinition of the list nth function
authorJoe Leslie-Hurd <joe@gilith.com>
licenseHOLLight
provenanceHOL Light theory extracted on 2012-12-02
requiresbool
list-dest
list-length
natural
showData.Bool
Data.List
Number.Natural

Files

Defined Constant

Theorems

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

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

External Type Operators

External Constants

Assumptions

() = λp. p ((select) p)

t. (x. t) t

() = λp. p = λx.

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

() = λp. q. (x. p x q) q

p. (x. y. p x y) y. x. p x (y x)

(∃!) = λp. () p x y. p x p y x = y

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