Package monoid-thm: Properties of monoids
Information
| name | monoid-thm |
| version | 1.6 |
| description | Properties of monoids |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2014-11-01 |
| checksum | b81c1f6696b4bc41eb1c617ace09842a38896ae8 |
| requires | base monoid-witness |
| show | Algebra.Monoid Data.Bool |
Files
- Package tarball monoid-thm-1.6.tgz
- Theory source file monoid-thm.thy (included in the package tarball)
Theorems
⊦ ∀x. 0 + x = x + 0
⊦ ∀x. x + 0 = 0 + x
⊦ ∀x y z. x + z = z + x ∧ y + z = z + y ⇒ x + y + z = z + (x + y)
⊦ ∀x y z. z + x = x + z ∧ z + y = y + z ⇒ z + (x + y) = x + y + z
External Type Operators
- →
- bool
- Algebra
- Monoid
- monoid
- Monoid
External Constants
- =
- Algebra
- Monoid
- +
- 0
- Monoid
- Data
- Bool
- ∀
- ∧
- ⇒
- ⊤
- Bool
Assumptions
⊦ ⊤
⊦ ∀t. (∀x. t) ⇔ t
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀x. 0 + x = x
⊦ ∀x. x + 0 = x
⊦ (⇒) = 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 ⊤ ⊤
⊦ ∀x y z. x + y + z = x + (y + z)