Package axiom: Standard axioms
Information
| name | axiom |
| version | 1.12 |
| description | Standard axioms |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| requires | bool function |
| show | Data.Bool Function |
Files
- Package tarball axiom-1.12.tgz
- Theory source file axiom.thy (included in the package tarball)
Theorems
⊦ ∀t. (λx. t x) = t
⊦ ∃f. injective f ∧ ¬surjective f
⊦ ∀p x. p x ⇒ p ((select) p)
External Type Operators
- →
- bool
- ind
External Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ¬
- ⊥
- ⊤
- Bool
- Function
- injective
- surjective
Assumptions
⊦ AXIOM OF EXTENSIONALITY
⊦ AXIOM OF CHOICE
⊦ AXIOM OF INFINITY
⊦ ⊤
⊦ ⊥ ⇔ ∀p. p
⊦ (¬) = λp. p ⇒ ⊥
⊦ ⊤ ⇔ (λp. p) = λp. p
⊦ (∀) = λp. p = λx. ⊤
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ ∀f. surjective f ⇔ ∀y. ∃x. y = f x
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀f. injective f ⇔ ∀x1 x2. f x1 = f x2 ⇒ x1 = x2