Theorems · Theorem · ring theory
commute_unitary_iff_star_left_conjugate
∀ {R : Type u_1} [inst : Monoid R] [inst_1 : StarMul R] {x u : R}, u ∈ unitary R → (Commute u x ↔ star u * x * u = x)- Defined in
- Mathlib.Algebra.Star.Unitary
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
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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_inv_mul_cancelproof · cited by 2
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