Package bool-ext: Extensional boolean theorems
Information
| name | bool-ext |
| version | 1.5 |
| description | Extensional boolean theorems |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-09-21 |
| requires | bool-def bool-int axiom-extensionality |
| show | Data.Bool |
Files
- Package tarball bool-ext-1.5.tgz
- Theory file bool-ext.thy (included in the package tarball)
Theorems
⊦ ∀f g. f = g ⇔ ∀x. f x = g x
⊦ ∀f g. (∀x. f x = g x) ⇒ f = g
Input Type Operators
- →
- bool
Input Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- ¬
- F
- T
- Bool
Assumptions
⊦ T
⊦ ∀t. (λx. t x) = t
⊦ (∀) = λp. p = λx. T
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f T T
⊦ ∀t. (T ⇒ t ⇔ t) ∧ (t ⇒ T ⇔ T) ∧ (F ⇒ t ⇔ T) ∧ (t ⇒ t ⇔ T) ∧ (t ⇒ F ⇔ ¬t)