Package list-thm: Properties of list types
Information
| name | list-thm |
| version | 1.51 |
| description | Properties of list types |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2014-06-12 |
| requires | bool list-def natural pair |
| show | Data.Bool Data.List Data.Pair Number.Natural |
Files
- Package tarball list-thm-1.51.tgz
- Theory source file list-thm.thy (included in the package tarball)
Theorems
⊦ ∀h t. ¬(h :: t = [])
⊦ ∀l. l = [] ∨ ∃h t. l = h :: t
⊦ ∀h1 h2 t1 t2. h1 :: t1 = h2 :: t2 ⇔ h1 = h2 ∧ t1 = t2
External Type Operators
- →
- bool
- Data
- List
- list
- Pair
- ×
- List
- Number
- Natural
- natural
- Natural
External Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∨
- ¬
- ⊥
- ⊤
- List
- ::
- []
- Pair
- ,
- Bool
- Number
- Natural
- +
- <
- ≤
- bit0
- bit1
- suc
- zero
- Natural
Assumptions
⊦ ⊤
⊦ ¬⊥ ⇔ ⊤
⊦ ¬⊤ ⇔ ⊥
⊦ bit0 0 = 0
⊦ ⊥ ⇔ ∀p. p
⊦ (¬) = λp. p ⇒ ⊥
⊦ ∀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
⊦ (∨) = 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
⊦ ∀p. p [] ∧ (∀h t. p t ⇒ p (h :: t)) ⇒ ∀l. p l
⊦ ∀a b a' b'. (a, b) = (a', b') ⇔ a = a' ∧ b = b'
⊦ ∀b f. ∃fn. fn [] = b ∧ ∀h t. fn (h :: t) = f h t (fn t)