Package monoid-comm-mult-thm: Properties of commutative monoid multiplication
Information
| name | monoid-comm-mult-thm |
| version | 1.2 |
| description | Properties of commutative monoid multiplication |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2013-03-09 |
| checksum | efb821301c5da9df182bf6c0938e0cdba15f4863 |
| requires | base monoid-mult-thm |
| show | Algebra.Monoid Data.Bool Number.Natural |
Files
- Package tarball monoid-comm-mult-thm-1.2.tgz
- Theory source file monoid-comm-mult-thm.thy (included in the package tarball)
Theorems
⊦ ∀n. 0 * n = 0
⊦ ∀x. x * 1 = x
⊦ ∀x. x * 2 = x + x
⊦ ∀x n. x * suc n = x * n + x
⊦ ∀x m n. x * (m * n) = x * m * n
⊦ ∀x m n. x * (m + n) = x * m + x * n
External Type Operators
- →
- bool
- Algebra
- Monoid
- monoid
- Monoid
- Number
- Natural
- natural
- Natural
External Constants
- =
- Algebra
- Monoid
- *
- +
- 0
- Monoid
- Data
- Bool
- ∀
- Bool
- Number
- Natural
- *
- +
- bit0
- bit1
- suc
- zero
- Natural
Assumptions
⊦ ∀n. 0 * n = 0
⊦ ∀x. x * 1 = x
⊦ ∀x. x * 2 = x + x
⊦ ∀x n. x * suc n = x * n + x
⊦ ∀x m n. x * (m * n) = x * m * n
⊦ ∀x m n. x * (m + n) = x * m + x * n