Theorems · Theorem · ring theory

AddMonoidAlgebra.coeff_single_mul_eq_mul_coeff

∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] {x : AddMonoidAlgebra R M} {r : R} {m m₁ : M} [inst_1 : Add M]
  (m₂ : M),
  (∀ m' ∈ x.coeff.support, m + m' = m₁ ↔ m' = m₂) → (AddMonoidAlgebra.single m r * x).coeff m₁ = r * x.coeff m₂

Defined in

Mathlib.Algebra.MonoidAlgebra.Defs

Cited by

3 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAdd