Package natural-sub-def: Definition of natural number subtraction

Information

namenatural-sub-def
version1.20
descriptionDefinition of natural number subtraction
authorJoe Hurd <joe@gilith.com>
licenseMIT
provenanceHOL Light theory extracted on 2012-03-26
requiresbool
natural-add
natural-def
natural-dest
natural-thm
showData.Bool
Number.Natural

Files

Defined Constant

Theorem

m n. m + n - n = m

Input Type Operators

Input Constants

Assumptions

() = λp. p ((select) p)

() = λp. p = λx.

n. pre (suc n) = n

m. m + 0 = m

() = λp q. p q p

() = λp q. (λf. f p q) = λf. f

() = λp. q. (x. p x q) q

m n. m + suc n = suc (m + n)

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

p. p 0 (n. p n p (suc n)) n. p n

(∃!) = λp. () p x y. p x p y x = y

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