Theorems · Theorem · ring theory
MonoidAlgebra.smul_single
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] {A : Type u_8} [inst_1 : SMulZeroClass A R] (a : A) (m : M) (r : R),
a • MonoidAlgebra.single m r = MonoidAlgebra.single m (a • r)- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringSMulZeroClass
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.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Finsupp.singleproof · cited by 943
- MonoidAlgebrastatement · cited by 590
- Finsupp.extproof · cited by 399
- MonoidAlgebra.singlestatement · cited by 253
- SMulZeroClassstatement and proof · cited by 213
- MonoidAlgebra.extproof · cited by 78
- Finsupp.smul_singleproof · cited by 48
Cited by10
Results whose statement or proof uses this declaration.
- MonoidAlgebra.induction_onproof · cited by 6
- Rep.standardComplex.d_eqproof · cited by 1
- MonoidAlgebra.isGroupLikeElem_iff_mem_range_single_oneproof · cited by 1
- MonoidAlgebra.single_mapDomainOfBialgHomproof · cited by 1
- Representation.leftRegular_norm_eq_zero_iffproof · cited by 1
- Rep.standardComplex.d_singleproof · cited by 0
- MonoidAlgebra.smul_single'proof · cited by 0
- MonoidAlgebra.smul_ofproof · cited by 0
- MonoidAlgebra.liftNC_smulproof · cited by 0
- MonoidAlgebra.span_isGroupLikeElemproof · cited by 0