Package list-dest-thm: Properties of list type destructors
Information
| name | list-dest-thm |
| version | 1.9 |
| description | Properties of list type destructors |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-12-18 |
| requires | bool list-def list-thm list-dest-def |
| show | Data.Bool Data.List |
Files
- Package tarball list-dest-thm-1.9.tgz
- Theory file list-dest-thm.thy (included in the package tarball)
Theorems
⊦ ∀l. null l ⇔ l = []
⊦ ∀l. case [] (::) l = l
⊦ ∀l. ¬(l = []) ⇒ head l :: tail l = l
Input Type Operators
- →
- bool
- Data
- List
- list
- List
Input Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∨
- ¬
- F
- T
- List
- ::
- []
- case
- head
- null
- tail
- Bool
Assumptions
⊦ T
⊦ null []
⊦ ¬F ⇔ T
⊦ ¬T ⇔ F
⊦ F ⇔ ∀p. p
⊦ (¬) = λp. p ⇒ F
⊦ (∀) = λp. p = λx. T
⊦ ∀t. (T ⇔ t) ⇔ t
⊦ ∀t. F ⇒ t ⇔ T
⊦ ∀t. T ⇒ t ⇔ t
⊦ ∀t. (F ⇔ t) ⇔ ¬t
⊦ ∀h t. ¬null (h :: t)
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀h t. ¬(h :: t = [])
⊦ ∀h t. head (h :: t) = h
⊦ ∀h t. tail (h :: t) = t
⊦ ∀b f. case b f [] = b
⊦ (∧) = λp q. (λf. f p q) = λf. f T T
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀x. x = [] ∨ ∃a0 a1. x = a0 :: a1
⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r
⊦ ∀b f h t. case b f (h :: t) = f h t
⊦ ∀P. P [] ∧ (∀a0 a1. P a1 ⇒ P (a0 :: a1)) ⇒ ∀x. P x