Theorems · Theorem · ring theory
Algebra.smul_mul_assoc
∀ {R : Type u} {A : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (r : R) (x y : A),
r • x * y = r • (x * y)This is just a special case of the global smul_mul_assoc lemma that requires less typeclass
search (and was here first).
- Defined in
- Mathlib.Algebra.Algebra.Defs
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses no axioms
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- smul_mul_assocproof · cited by 77
Cited by30
Results whose statement or proof uses this declaration.
- Algebra.traceMatrix_of_matrix_vecMulproof · cited by 2
- dvd_coeff_zero_of_aeval_eq_prime_smul_of_minpoly_isEisensteinAtproof · cited by 1
- IsStrictlyPositive.smulproof · cited by 1
- HahnSeries.SummableFamily.hsum_powerSeriesFamily_mulproof · cited by 1
- RingHom.SurjectiveOnStalks.baseChangeproof · cited by 1
- Submodule.ker_unitsToPicproof · cited by 1
- PowerBasis.repr_mul_isIntegralproof · cited by 1
- HahnSeries.SummableFamily.support_powerSeriesFamily_subsetproof · cited by 1
- Matrix.PosDef.smulproof · cited by 1
- Matrix.ProjectiveSpecialLinearGroup.toPGL_surj_of_rootsproof · cited by 1
- tendsto_integral_mul_one_add_inv_smul_sq_powproof · cited by 1
- Polynomial.aeval_eq_smevalproof · cited by 1