Package list-zip-def: Definition of the list zip function
Information
| name | list-zip-def |
| version | 1.12 |
| description | Definition of the list zip function |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2012-08-06 |
| requires | bool list-def list-dest list-length pair |
| show | Data.Bool Data.List Data.Pair Number.Natural |
Files
- Package tarball list-zip-def-1.12.tgz
- Theory file list-zip-def.thy (included in the package tarball)
Defined Constants
- Data
- List
- zip
- zipWith
- List
Theorems
⊦ ∀f. zipWith f [] [] = []
⊦ ∀l1 l2. zip l1 l2 = zipWith , l1 l2
⊦ ∀f h1 h2 t1 t2.
length t1 = length t2 ⇒
zipWith f (h1 :: t1) (h2 :: t2) = f h1 h2 :: zipWith f t1 t2
Input Type Operators
- →
- bool
- Data
- List
- list
- Pair
- ×
- List
- Number
- Natural
- natural
- Natural
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ⊤
- List
- ::
- []
- head
- length
- tail
- Pair
- ,
- Bool
Assumptions
⊦ ⊤
⊦ (∃) = λp. p ((select) p)
⊦ ∀t. (∀x. t) ⇔ t
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀t. t ⇒ ⊤ ⇔ ⊤
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀h t. head (h :: t) = h
⊦ ∀h t. tail (h :: t) = t
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀p. (∀x. ∃y. p x y) ⇔ ∃y. ∀x. p x (y x)
⊦ ∀b f. ∃fn. fn [] = b ∧ ∀h t. fn (h :: t) = f h t (fn t)