Package natural-order-def: Definition of natural number orderings

Information

namenatural-order-def
version1.23
descriptionDefinition of natural number orderings
authorJoe Hurd <joe@gilith.com>
licenseHOLLight
provenanceHOL Light theory extracted on 2012-06-16
requiresbool
natural-thm
showData.Bool
Number.Natural

Files

Defined Constants

Theorems

m. ¬(m < 0)

m. m 0 m = 0

m n. m > n n < m

m n. m n n m

m n. m < suc n m = n m < n

m n. m suc n m = suc n m n

Input Type Operators

Input Constants

Assumptions

() = λp. p ((select) p)

() = λp. p = λx.

t. (t ) ¬t

() = λp q. p q p

() = 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