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Theorems · Theorem · ring theory

AddMonoidAlgebra.coeff_single_zero_mul

∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddZeroClass M] (x : AddMonoidAlgebra R M) (r : R)
  (m : M), (AddMonoidAlgebra.single 0 r * x).coeff m = r * x.coeff m
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
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.coeff_C_mul · cited by 55Polynomial.coeff_C_mulDFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringFinsupp · cited by 5255Finsuppzero_add · cited by 2366zero_addAddZeroClass · cited by 1237AddZeroClassAddMonoidAlgebra · cited by 649AddMonoidAlgebraAddMonoidAlgebra.coeff · cited by 365AddMonoidAlgebra.coeffAddMonoidAlgebra.single · cited by 250AddMonoidAlgebra.singleFinsupp.mem_support_iff · cited by 89Finsupp.mem_support_iffAddMonoidAlgebra.coeff_single_mul_eq_mul_coeff · cited by 3AddMonoidAlgebra.coeff_si…AddMonoidAlgebra.coeff_single…CITED BYCITES

Cites10

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Cited by1

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