Package option-thm: Properties of option types

Information

nameoption-thm
version1.53
descriptionProperties of option types
authorJoe Leslie-Hurd <joe@gilith.com>
licenseHOLLight
provenanceHOL Light theory extracted on 2014-11-01
checksum0269331160032c8448335045747d281396643630
requiresbool
natural
option-def
showData.Bool
Data.Option
Number.Natural

Files

Theorems

a. ¬(some a = none)

x. x = none a. x = some a

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

External Type Operators

External Constants

Assumptions

¬

¬

bit0 0 = 0

t. (x. t) t

t. (λx. t x) = t

() = λp. p = λx.

t. ¬¬t t

t. t

t. t t

t. t t

t. t

n. 0 + n = n

t. ( t) ¬t

t. (t ) ¬t

t. t ¬t

n. bit1 n = suc (bit0 n)

() = λp q. p q p

t. (t ) (t )

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

f y. (let x y in f x) = f y

m n. m + n = n + m

m n. ¬(m n) n < m

() = λp q. (λf. f p q) = λf. f

p. ¬(x. p x) x. ¬p x

() = λp. q. (x. p x q) q

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

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

t1 t2. ¬(t1 t2) ¬t1 ¬t2

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

() = λp q. r. (p r) (q r) r

m n. m n n m m = n

m n. m < n d. n = m + suc d

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

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