Theorems · Theorem · ring theory
commute_unitary_iff_star_right_conjugate
∀ {R : Type u_1} [inst : Monoid R] [inst_1 : StarMul R] {x u : R}, u ∈ unitary R → (Commute u x ↔ u * x * star u = x)- Defined in
- Mathlib.Algebra.Star.Unitary
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- Star.starstatement · cited by 1,082
- Commutestatement and proof · cited by 639
- unitarystatement and proof · cited by 207
- StarMulstatement and proof · cited by 195
- Unitary.val_toUnits_applyproof · cited by 7
- Unitary.val_inv_toUnits_applyproof · cited by 4
- Units.commute_iff_mul_inv_cancelproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.