Package list-dest-def: Definition of list type destructors
Information
| name | list-dest-def |
| version | 1.35 |
| description | Definition of list type destructors |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2012-06-08 |
| requires | bool list-def |
| show | Data.Bool Data.List |
Files
- Package tarball list-dest-def-1.35.tgz
- Theory file list-dest-def.thy (included in the package tarball)
Defined Constants
- Data
- List
- case
- head
- null
- tail
- List
Theorems
⊦ null []
⊦ ∀h t. ¬null (h :: t)
⊦ ∀h t. head (h :: t) = h
⊦ ∀h t. tail (h :: t) = t
⊦ ∀b f. case b f [] = b
⊦ ∀b f h t. case b f (h :: t) = f h t
Input Type Operators
- →
- bool
- Data
- List
- list
- List
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ¬
- ⊥
- ⊤
- List
- ::
- []
- Bool
Assumptions
⊦ ⊤
⊦ (∃) = λp. p ((select) p)
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀t. (t ⇔ ⊤) ⇔ t
⊦ ∀t. (t ⇔ ⊥) ⇔ ¬t
⊦ (⇒) = 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)