Theorems · Theorem · ring theory
StarMul.star_mul
∀ {R : Type u} {inst : Mul R} [self : StarMul R] (r s : R), star (r * s) = star s * star rstar skew-distributes over multiplication.
- Defined in
- Mathlib.Algebra.Star.Basic
- Cited by
- 72 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- StarMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by72
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.star_mul_selfproof · cited by 12
- Matrix.conjTranspose_mulproof · cited by 9
- star_le_star_iffproof · cited by 6
- star_left_conjugate_nonnegproof · cited by 6
- star_mul'proof · cited by 5
- IsSelfAdjoint.commute_iffproof · cited by 5
- CStarRing.norm_coe_unitary_mulproof · cited by 4
- IsStarProjection.le_tfaeproof · cited by 4
- CStarAlgebra.inv_le_invproof · cited by 3
- Matrix.star_dotProduct_starproof · cited by 3
- CFC.norm_star_mul_mul_self_of_nonnegproof · cited by 3
- IsStarProjection.sub_of_mul_eq_leftproof · cited by 3