Theorems · Theorem · ring theory
MonoidAlgebra.single_mul_single
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : Mul M] (m₁ m₂ : M) (r₁ r₂ : R),
MonoidAlgebra.single m₁ r₁ * MonoidAlgebra.single m₂ r₂ = MonoidAlgebra.single (m₁ * m₂) (r₁ * r₂)- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- Finsupp.singleproof · cited by 943
- MonoidAlgebrastatement · cited by 590
- Finsupp.sumproof · cited by 481
- MonoidAlgebra.singlestatement and proof · cited by 253
- Finsupp.sum_single_indexproof · cited by 130
- MonoidAlgebra.mul_defproof · cited by 7
- MonoidAlgebra.single_zeroproof · cited by 5
Cited by14
Results whose statement or proof uses this declaration.
- MonoidAlgebra.ringHom_extproof · cited by 7
- MonoidAlgebra.algHom_extproof · cited by 7
- LinearMap.conjugate_iproof · cited by 1
- MonoidAlgebra.prod_singleproof · cited by 1
- MonoidAlgebra.single_commute_singleproof · cited by 1
- MonoidAlgebra.rTensorEquivAlgEquiv.invFun_tmulproof · cited by 1
- GroupAlgebra.mul_average_leftproof · cited by 1
- MonoidAlgebra.single_eq_algebraMap_mul_ofproof · cited by 0
- MonoidAlgebra.freeAlgebra_lift_of_surjective_of_closureproof · cited by 0
- MonoidAlgebra.mapDomainBialgHom_mulproof · cited by 0
- MonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closureproof · cited by 0
- GroupAlgebra.mul_average_rightproof · cited by 0