Package list-filter-def: Definition of the list filter function
Information
| name | list-filter-def |
| version | 1.30 |
| description | Definition of the list filter function |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2012-04-05 |
| requires | bool list-def |
| show | Data.Bool Data.List |
Files
- Package tarball list-filter-def-1.30.tgz
- Theory file list-filter-def.thy (included in the package tarball)
Defined Constant
- Data
- List
- filter
- List
Theorems
⊦ ∀p. filter p [] = []
⊦ ∀p h t. filter p (h :: t) = if p h then h :: filter p t else filter p t
Input Type Operators
- →
- bool
- Data
- List
- list
- List
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- cond
- ⊤
- List
- ::
- []
- Bool
Assumptions
⊦ ⊤
⊦ (∃) = λp. p ((select) p)
⊦ (∀) = λp. p = λx. ⊤
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = 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)