Theorems · Theorem · ring theory
AddMonoidAlgebra.coeff_mul_single_zero
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddZeroClass M] (x : AddMonoidAlgebra R M) (r : R)
(m : M), (x * AddMonoidAlgebra.single 0 r).coeff m = x.coeff m * r- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddZeroClass
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.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Finsuppstatement · cited by 5,255
- add_zeroproof · cited by 2,707
- AddZeroClassstatement and proof · cited by 1,237
- AddMonoidAlgebrastatement and proof · cited by 649
- AddMonoidAlgebra.coeffstatement and proof · cited by 365
- AddMonoidAlgebra.singlestatement · cited by 250
- Finsupp.mem_support_iffproof · cited by 89
- AddMonoidAlgebra.coeff_mul_single_eq_coeff_mulproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.coeff_mul_Cproof · cited by 20