Package monoid-comm-thm: Properties of commutative monoids
Information
| name | monoid-comm-thm |
| version | 1.7 |
| description | Properties of commutative monoids |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2014-11-01 |
| checksum | f37cbe5d981f18bb4ec0949540b58fbe8b6b1fdd |
| requires | bool monoid-comm-witness monoid-witness |
| show | Algebra.Monoid Data.Bool |
Files
- Package tarball monoid-comm-thm-1.7.tgz
- Theory source file monoid-comm-thm.thy (included in the package tarball)
Theorems
⊦ ∀x. x + 0 = x
⊦ ∀x y z. x + (y + z) = y + (x + z)
External Type Operators
- →
- bool
- Algebra
- Monoid
- monoid
- Monoid
External Constants
- =
- Algebra
- Monoid
- +
- 0
- Monoid
- Data
- Bool
- ∀
- ∧
- ⇒
- ⊤
- Bool
Assumptions
⊦ ⊤
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀x. x + 0 = x
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀x y. x + y = y + x
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ ∀x y z. x + y + z = x + (y + z)