Theorems · Theorem · ring theory
MonoidAlgebra.single_mul_apply_aux
Deprecated since 2026-06-18Use MonoidAlgebra.coeff_single_mul_eq_mul_coeff instead.
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] {x : MonoidAlgebra R M} {r : R} {m m₁ : M} [inst_1 : Mul M]
(m₂ : M), (∀ m' ∈ x.coeff.support, m * m' = m₁ ↔ m' = m₂) → (MonoidAlgebra.single m r * x).coeff m₁ = r * x.coeff m₂Alias of MonoidAlgebra.coeff_single_mul_eq_mul_coeff.
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement · cited by 13,802
- Finsetstatement · cited by 13,712
- Finsuppstatement · cited by 5,255
- Finsupp.supportstatement · cited by 828
- MonoidAlgebrastatement · cited by 590
- MonoidAlgebra.singlestatement · cited by 253
- MonoidAlgebra.coeffstatement · cited by 224
- MonoidAlgebra.coeff_single_mul_eq_mul_coeffproof · cited by 4
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