Package list-take-drop-def: Definition of the list take and drop functions
Information
| name | list-take-drop-def |
| version | 1.36 |
| description | Definition of the list take and drop functions |
| author | Joe Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2012-03-24 |
| requires | bool list-dest natural |
| show | Data.Bool Data.List Number.Natural |
Files
- Package tarball list-take-drop-def-1.36.tgz
- Theory file list-take-drop-def.thy (included in the package tarball)
Defined Constants
- Data
- List
- drop
- take
- List
Theorems
⊦ ∀l. drop 0 l = l
⊦ ∀l. take 0 l = []
⊦ ∀n h t. n ≤ length t ⇒ drop (suc n) (h :: t) = drop n t
⊦ ∀n h t. n ≤ length t ⇒ take (suc n) (h :: t) = h :: take n t
Input Type Operators
- →
- bool
- Data
- List
- list
- List
- Number
- Natural
- natural
- Natural
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∃!
- ⊤
- List
- ::
- []
- head
- length
- tail
- Bool
- Number
- Natural
- ≤
- suc
- zero
- Natural
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)
⊦ (∃!) = λp. (∃) p ∧ ∀x y. p x ∧ p y ⇒ x = y
⊦ ∀e f. ∃!fn. fn 0 = e ∧ ∀n. fn (suc n) = f (fn n) n