Package axiom-choice: Axiom of Choice
Information
| name | axiom-choice |
| version | 1.5 |
| description | Axiom of Choice |
| author | Joe Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2011-07-20 |
| requires | bool-def |
| show | Data.Bool |
Files
- Package tarball axiom-choice-1.5.tgz
- Theory file axiom-choice.thy (included in the package tarball)
Theorem
⊦ ∀p x. p x ⇒ p ((select) p)
Input Type Operators
- →
- bool
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- T
- Bool
Assumptions
⊦ T ⇔ (λp. p) = λp. p
⊦ (∀) = λp. p = λx. T
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f T T
⊦ let a d ←
let e g ←
(let h ← d g in
λi.
(let j ← h in
λk. (λl. l j k) = λm. m ((λc. c) = λc. c) ((λc. c) = λc. c))
i ⇔ h) (d ((select) d)) in
e = (λf. (λc. c) = λc. c) in
a = λb. (λc. c) = λc. c