Theorems · Theorem · ring theory
SkewMonoidAlgebra.smul_single
∀ {k : Type u_1} {G : Type u_2} [inst : AddMonoid k] {S : Type u_3} [inst_1 : SMulZeroClass S k] (s : S) (a : G)
(b : k), s • SkewMonoidAlgebra.single a b = SkewMonoidAlgebra.single a (s • b)- Defined in
- Mathlib.Algebra.SkewMonoidAlgebra.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoidSMulZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- Finsupp.singleproof · cited by 943
- SkewMonoidAlgebrastatement · cited by 216
- SMulZeroClassstatement and proof · cited by 213
- SkewMonoidAlgebra.singlestatement and proof · cited by 83
- Finsupp.smul_singleproof · cited by 48
- SkewMonoidAlgebra.coeff_injectiveproof · cited by 7
- SkewMonoidAlgebra.coeff_smulproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- SkewMonoidAlgebra.liftNC_smulproof · cited by 0
- IsSMulRegular.skewMonoidAlgebra_iffproof · cited by 0
- SkewMonoidAlgebra.smul_ofproof · cited by 0
- SkewMonoidAlgebra.mem_span_supportproof · cited by 0
- SkewPolynomial.smul_X_eq_monomialproof · cited by 0
- SkewPolynomial.smul_monomialproof · cited by 0