Package option-thm: Properties of option types

Information

nameoption-thm
version1.35
descriptionProperties of option types
authorJoe Hurd <joe@gilith.com>
licenseHOLLight
provenanceHOL Light theory extracted on 2012-05-18
requiresbool
natural
option-def
showData.Bool
Data.Option
Number.Natural

Files

Theorems

a'. ¬(none = some a')

x. x = none a. x = some a

a a'. some a = some a' a = a'

Input Type Operators

Input Constants

Assumptions

¬

¬

bit0 0 = 0

n. 0 n

p. p

(¬) = λp. p

t. (x. t) t

() = λp. p = λx.

t. ( t) t

t. (t ) t

t. t t

t. t t

t. t t

t. t

n. ¬(suc n = 0)

n. 0 + n = n

t. (t ) ¬t

t. t ¬t

n. bit1 n = suc (bit0 n)

() = λp q. p q p

n. even (suc n) ¬even n

m. m 0 m = 0

n. bit0 (suc n) = suc (suc (bit0 n))

t1 t2. t1 t2 t2 t1

n. 2 * n = n + n

m n. suc m n m < n

() = λp q. (λf. f p q) = λf. f

() = λp. q. (x. p x q) q

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

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

m n. suc m = suc n m = n

m n. even (m * n) even m even n

m n. even (m + n) even m even n

p. p none (a. p (some a)) x. p x

() = λp q. r. (p r) (q r) r

m n. m n m < n m = n

m n. m n n m m = n

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

m n. m * n = 0 m = 0 n = 0

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

b f. fn. fn none = b a. fn (some a) = f a

m n p. m * n = m * p m = 0 n = p

m n p. m * n m * p m = 0 n p

m n p. m * n < m * p ¬(m = 0) n < p