Package natural-funpow: Function power

Information

namenatural-funpow
version1.1
descriptionFunction power
authorJoe Hurd <joe@gilith.com>
licenseMIT
requiresbool
function
natural-add
natural-def
natural-mult
natural-numeral
natural-thm
showData.Bool
Function
Number.Natural

Files

Defined Constant

Theorems

n. id n = id

f. f 0 = id

f. f 1 = f

f n. f suc n = f f n

f n. f suc n = f n f

f n x. (f suc n) x = f ((f n) x)

f n x. (f suc n) x = (f n) (f x)

f m n. f (m * n) = (f m) n

f m n. f (m + n) = f m f n

Input Type Operators

Input Constants

Assumptions

bit0 0 = 0

() = λp. p ((select) p)

t. (x. t) t

() = λp. p = λx.

m. m * 0 = 0

m. m + 0 = m

f. f id = f

f. id f = f

n. bit1 n = suc (bit0 n)

() = 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)

f g x. (f g) x = f (g x)

m n. m * suc n = m + m * n

f g h. f g h = f (g h)

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