Package option-thm: option-thm

Information

nameoption-thm
version1.9
descriptionoption-thm
authorJoe Hurd <joe@gilith.com>
licenseHOLLight
provenanceHOL Light theory extracted on 2011-07-25
showData.Bool

Files

Theorems

a'. ¬(Data.Option.none = Data.Option.some a')

x. x = Data.Option.none a. x = Data.Option.some a

a a'. Data.Option.some a = Data.Option.some a' a = a'

Input Type Operators

Input Constants

Assumptions

T

n. Number.Natural.≤ 0 n

F p. p

(~) = λp. p F

t. (x. t) t

() = λp. p = λx. T

x. x = x T

n. ¬(Number.Natural.suc n = 0)

n. Number.Natural.bit0 n = Number.Natural.+ n n

() = λp q. p q p

n. Number.Natural.bit1 n = Number.Natural.suc (Number.Natural.+ n n)

(¬T F) (¬F T)

t1 t2. t1 t2 t2 t1

n. Number.Natural.* 2 n = Number.Natural.+ n n

m n. Number.Natural.≤ (Number.Natural.suc m) n Number.Natural.< m n

() = λp q. (λf. f p q) = λf. f T T

() = λP. q. (x. P x q) q

m n. Number.Natural.suc m = Number.Natural.suc n m = n

m n.
    Number.Natural.even (Number.Natural.* m n)
    Number.Natural.even m Number.Natural.even n

m n.
    Number.Natural.even (Number.Natural.+ m n) Number.Natural.even m
    Number.Natural.even n

P. P Data.Option.none (a. P (Data.Option.some a)) x. P x

() = λp q. r. (p r) (q r) r

(Number.Natural.even 0 T)
  n. Number.Natural.even (Number.Natural.suc n) ¬Number.Natural.even n

m n. Number.Natural.≤ m n Number.Natural.< m n m = n

m n. Number.Natural.≤ m n Number.Natural.≤ n m m = n

m n. Number.Natural.* m n = 0 m = 0 n = 0

NONE' SOME'.
    fn.
      fn Data.Option.none = NONE' a. fn (Data.Option.some a) = SOME' a

m n p. Number.Natural.* m n = Number.Natural.* m p m = 0 n = p

m n p.
    Number.Natural.≤ (Number.Natural.* m n) (Number.Natural.* m p)
    m = 0 Number.Natural.≤ n p

m n p.
    Number.Natural.< (Number.Natural.* m n) (Number.Natural.* m p)
    ¬(m = 0) Number.Natural.< n p

(m. Number.Natural.≤ m 0 m = 0)
  m n.
    Number.Natural.≤ m (Number.Natural.suc n)
    m = Number.Natural.suc n Number.Natural.≤ m n

t. ((T t) t) ((t T) t) ((F t) ¬t) ((t F) ¬t)

t. (T t t) (t T t) (F t F) (t F F) (t t t)

t. (T t T) (t T T) (F t t) (t F t) (t t t)

t. (T t t) (t T T) (F t T) (t t T) (t F ¬t)

(n. Number.Natural.+ 0 n = n) (m. Number.Natural.+ m 0 = m)
  (m n.
     Number.Natural.+ (Number.Natural.suc m) n =
     Number.Natural.suc (Number.Natural.+ m n))
  m n.
    Number.Natural.+ m (Number.Natural.suc n) =
    Number.Natural.suc (Number.Natural.+ m n)