Theorems · Theorem · ring theory
MonoidAlgebra.coeff_single_one_mul
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : MulOneClass M] (x : MonoidAlgebra R M) (r : R) (m : M),
(MonoidAlgebra.single 1 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
- SemiringMulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- one_mulproof · cited by 2,841
- MulOneClassstatement and proof · cited by 1,018
- MonoidAlgebrastatement and proof · cited by 590
- MonoidAlgebra.singlestatement · cited by 253
- MonoidAlgebra.coeffstatement and proof · cited by 224
- MonoidAlgebra.coeff_single_mul_eq_mul_coeffproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- MonoidAlgebra.single_one_mul_applyproof · cited by 0