Package monoid-mult-def: Definition of monoid multiplication
Information
| name | monoid-mult-def |
| version | 1.9 |
| description | Definition of monoid multiplication |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2014-11-04 |
| checksum | f458d6973fdf3216542ffec5db0914741a79cf5d |
| requires | bool monoid-witness natural |
| show | Algebra.Monoid Data.Bool Number.Natural |
Files
- Package tarball monoid-mult-def-1.9.tgz
- Theory source file monoid-mult-def.thy (included in the package tarball)
Defined Constant
- Algebra
- Monoid
- *
- Monoid
Theorems
⊦ ∀x. x * 0 = 0
⊦ ∀x n. x * suc n = x + x * n
External Type Operators
- →
- bool
- Algebra
- Monoid
- monoid
- Monoid
- Number
- Natural
- natural
- Natural
External Constants
- =
- select
- Algebra
- Monoid
- +
- 0
- Monoid
- 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
⊦ (∃!) = λp. (∃) p ∧ ∀x y. p x ∧ p y ⇒ x = y
⊦ ∀e f. ∃!fn. fn 0 = e ∧ ∀n. fn (suc n) = f (fn n) n