Package group-thm: Consequences of the group axioms and subtraction
Information
| name | group-thm |
| version | 1.4 |
| description | Consequences of the group axioms and subtraction |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2012-09-25 |
| requires | bool group-witness |
| show | Algebra.Group Data.Bool |
Files
- Package tarball group-thm-1.4.tgz
- Theory source file group-thm.thy (included in the package tarball)
Theorems
⊦ ∀x. x + 0 = x
⊦ ∀x. x + ~x = 0
⊦ ∀x y. x + (~x + y) = y
⊦ ∀x y. ~x + (x + y) = y
External Type Operators
- →
- bool
- Algebra
- Group
- group
- Group
External Constants
- =
- Algebra
- Group
- +
- ~
- 0
- Group
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ⊤
- Bool
Assumptions
⊦ ⊤
⊦ ∀t. (∀x. t) ⇔ t
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀x. 0 + x = x
⊦ ∀x. ~x + x = 0
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀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)