Package natural-recursion: natural-recursion

Information

namenatural-recursion
version1.3
descriptionnatural-recursion
authorJoe Hurd <joe@gilith.com>
licenseHOLLight
provenanceHOL Light theory extracted on 2011-09-21
showData.Bool

Files

Theorem

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

Input Type Operators

Input Constants

Assumptions

T

F p. p

(¬) = λp. p F

a. ∃!x. x = a

t. (x. t) t

() = λp. p = λx. T

x. x = x T

n. ¬(Number.Natural.suc n = 0)

() = λp q. p q p

() = λp q. (λf. f p q) = λf. f T T

() = λP. q. (x. P x q) q

m n. Number.Natural.suc m = Number.Natural.suc n m = n

f g. f = g x. f x = g x

P a. (x. a = x P x) P a

() = λp q. r. (p r) (q r) r

P. P 0 (n. P n P (Number.Natural.suc n)) n. P n

P Q. (x. P x Q x) (x. P x) x. Q x

A B C D. (A B) (C D) A C B D

A B C D. (A B) (C D) A C B D

P. (x. ∃!y. P x y) f. x y. P x y f x = y

P. (∃!x. P x) (x. P x) x x'. P x P x' x = x'

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

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