Package bool-def: Boolean definitions
Information
| name | bool-def |
| version | 1.10 |
| description | Boolean definitions |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-12-18 |
| show | Data.Bool |
Files
- Package tarball bool-def-1.10.tgz
- Theory file bool-def.thy (included in the package tarball)
Defined Constants
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∃!
- ∨
- ¬
- cond
- ⊥
- ⊤
- Bool
Theorems
⊦ ⊥ ⇔ ∀p. p
⊦ (¬) = λp. p ⇒ ⊥
⊦ ⊤ ⇔ (λp. p) = λp. p
⊦ (∀) = λp. p = λx. ⊤
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r
⊦ (∃!) = λp. (∃) p ∧ ∀x y. p x ∧ p y ⇒ x = y
⊦ cond = λt t1 t2. select x. ((t ⇔ ⊤) ⇒ x = t1) ∧ ((t ⇔ ⊥) ⇒ x = t2)
Input Type Operators
- →
- bool
Input Constants
- =
- select