Package natural-def: natural-def

Information

namenatural-def
version1.4
descriptionnatural-def
authorJoe Hurd <joe@gilith.com>
licenseHOLLight
provenanceHOL Light theory extracted on 2011-07-25
showData.Bool

Files

Defined Type Operator

Defined Constants

Theorems

n. ¬(Number.Natural.suc n = 0)

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

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

Input Type Operators

Input Constants

Assumptions

T

F p. p

t. t ¬t

(~) = λp. p F

() = λP. P ((select) P)

t. (x. t) t

t. (λx. t x) = t

() = λp. p = λx. T

x. x = x T

f. Function.injective f ¬Function.surjective f

() = λp q. p q p

t. (t T) (t F)

(¬T F) (¬F T)

() = λp q. (λf. f p q) = λf. f T T

f. Function.surjective f y. x. y = f x

P. ¬(x. P x) x. ¬P x

P. ¬(x. P x) x. ¬P x

() = λP. q. (x. P x q) q

() = λp q. r. (p r) (q r) r

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

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

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

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

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

f. Function.injective f x1 x2. f x1 = f x2 x1 = x2

(t. ¬¬t t) (¬T F) (¬F T)

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

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

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

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

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

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)

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

p q r.
    (p q q p) ((p q) r p q r) (p q r q p r)
    (p p p) (p p q p q)