Theorems · Theorem · ring theory
MonoidAlgebra.coeff_single_mul_mul
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : Monoid M] [IsCancelMul M] (x : MonoidAlgebra R M) (r : R)
(m m' : M), (MonoidAlgebra.single m r * x).coeff (m * m') = r * x.coeff m'- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringMonoidIsCancelMul
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Cites9
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
- Monoidstatement and proof · cited by 3,887
- MonoidAlgebrastatement and proof · cited by 590
- MonoidAlgebra.singlestatement · cited by 253
- MonoidAlgebra.coeffstatement and proof · cited by 224
- IsCancelMulstatement and proof · cited by 32
- MonoidAlgebra.coeff_single_mul_eq_mul_coeffproof · cited by 4
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