Package group-abelian: Abelian groups
Information
| name | group-abelian |
| version | 1.9 |
| description | Abelian groups |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2012-12-02 |
| requires | bool group-thm group-witness |
| show | Algebra.Group Data.Bool |
Files
- Package tarball group-abelian-1.9.tgz
- Theory source file group-abelian.thy (included in the package tarball)
Theorem
⊦ ∀x y z. x + (y + z) = y + (x + z)
External Type Operators
- →
- bool
- Algebra
- Group
- group
- Group
External Constants
- =
- Algebra
- Group
- +
- ~
- 0
- Group
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ⊤
- Bool
Assumptions
⊦ ⊤
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀x. x + 0 = x
⊦ ∀x. x + ~x = 0
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀x y. x = y ⇒ y = x
⊦ ∀x y. x + y = y + x
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀x y z. x = y ∧ y = z ⇒ x = z
⊦ ∀x y z. x + y + z = x + (y + z)