Package list-dest-thm: Properties of list type destructors
Information
| name | list-dest-thm |
| version | 1.13 |
| description | Properties of list type destructors |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2012-03-24 |
| requires | bool list-def list-dest-def list-thm |
| show | Data.Bool Data.List |
Files
- Package tarball list-dest-thm-1.13.tgz
- Theory file list-dest-thm.thy (included in the package tarball)
Theorems
⊦ ∀l. null l ⇔ l = []
⊦ ∀l. case [] (::) l = l
⊦ ∀l. ¬null l ⇒ head l :: tail l = l
Input Type Operators
- →
- bool
- Data
- List
- list
- List
Input Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- ¬
- ⊥
- ⊤
- List
- ::
- []
- case
- head
- null
- tail
- Bool
Assumptions
⊦ ⊤
⊦ null []
⊦ ¬⊥ ⇔ ⊤
⊦ ¬⊤ ⇔ ⊥
⊦ ⊥ ⇔ ∀p. p
⊦ (¬) = λp. p ⇒ ⊥
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀t. (⊤ ⇔ t) ⇔ t
⊦ ∀t. ⊥ ⇒ t ⇔ ⊤
⊦ ∀t. ⊤ ⇒ t ⇔ t
⊦ ∀t. (⊥ ⇔ 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 ⊤ ⊤
⊦ ∀b f h t. case b f (h :: t) = f h t
⊦ ∀p. p [] ∧ (∀h t. p t ⇒ p (h :: t)) ⇒ ∀l. p l