Package group-mult-def: Definition of group multiplication
Information
| name | group-mult-def |
| version | 1.9 |
| description | Definition of group multiplication |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2012-12-02 |
| requires | bool group-witness natural |
| show | Algebra.Group Data.Bool Number.Natural |
Files
- Package tarball group-mult-def-1.9.tgz
- Theory source file group-mult-def.thy (included in the package tarball)
Defined Constant
- Algebra
- Group
- *
- Group
Theorems
⊦ ∀x. x * 0 = 0
⊦ ∀x n. x * suc n = x + x * n
External Type Operators
- →
- bool
- Algebra
- Group
- group
- Group
- Number
- Natural
- natural
- Natural
External Constants
- =
- select
- Algebra
- Group
- +
- 0
- Group
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∃!
- ⊤
- Bool
- Number
- Natural
- suc
- zero
- Natural
Assumptions
⊦ ⊤
⊦ (∃) = λp. p ((select) p)
⊦ (∀) = λp. p = λx. ⊤
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀p. (∀x. ∃y. p x y) ⇔ ∃y. ∀x. p x (y x)
⊦ (∃!) = λp. (∃) p ∧ ∀x y. p x ∧ p y ⇒ x = y
⊦ ∀e f. ∃!fn. fn 0 = e ∧ ∀n. fn (suc n) = f (fn n) n