Theorems · Inductive type · ring theory
KleeneAlgebra
Type u_5 → Type u_5
A Kleene algebra is an idempotent semiring with an additional unary operator kstar
(for Kleene star) that satisfies the following properties:
* 1 ≤ a∗
* a * a∗ ≤ a∗
* a∗ * a ≤ a∗
* If b * a ≤ b, then b * a∗ ≤ b
* If a * b ≤ b, then a∗ * b ≤ b
- Defined in
- Mathlib.Algebra.Order.Kleene
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 0 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by37
Results whose statement or proof uses this declaration.
- one_le_kstarstatement and proof · cited by 8
- le_kstarstatement and proof · cited by 3
- kstar_le_of_mul_le_leftstatement and proof · cited by 3
- kstar_mul_le_kstarstatement and proof · cited by 3
- mul_kstar_lestatement and proof · cited by 2
- mul_kstar_le_kstarstatement and proof · cited by 2
- mul_kstar_le_selfstatement and proof · cited by 2
- kstar_eq_onestatement and proof · cited by 2
- kstar_mul_kstarstatement and proof · cited by 2
- kstar_mul_lestatement and proof · cited by 2
- kstar_mul_le_selfstatement and proof · cited by 2
- KleeneAlgebra.one_le_kstarstatement and proof · cited by 1