Package list-quant-def: Definition of list quantifiers
Information
| name | list-quant-def |
| version | 1.28 |
| description | Definition of list quantifiers |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2012-02-10 |
| requires | bool list-def |
| show | Data.Bool Data.List |
Files
- Package tarball list-quant-def-1.28.tgz
- Theory file list-quant-def.thy (included in the package tarball)
Defined Constants
- Data
- List
- all
- exists
- List
Theorems
⊦ ∀p. all p []
⊦ ∀p. ¬exists p []
⊦ ∀p h t. all p (h :: t) ⇔ p h ∧ all p t
⊦ ∀p h t. exists p (h :: t) ⇔ p h ∨ exists p 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)
⊦ ∀NIL' CONS'.
∃fn. fn [] = NIL' ∧ ∀a0 a1. fn (a0 :: a1) = CONS' a0 a1 (fn a1)