Theorems · Theorem · ring theory
SkewMonoidAlgebra.coeff_mul_single_one
∀ {k : Type u_1} {G : Type u_2} [inst : Semiring k] [inst_1 : Monoid G] [inst_2 : MulSemiringAction G k]
(f : SkewMonoidAlgebra k G) (r : k) (x : G), (f * SkewMonoidAlgebra.single 1 r).coeff x = f.coeff x * x • r- Defined in
- Mathlib.Algebra.SkewMonoidAlgebra.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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 and proof · cited by 13,802
- Finsuppstatement · cited by 5,255
- Monoidstatement and proof · cited by 3,887
- mul_oneproof · cited by 3,885
- MulSemiringActionstatement and proof · cited by 423
- SkewMonoidAlgebrastatement and proof · cited by 216
- SkewMonoidAlgebra.coeffstatement · cited by 110
- SkewMonoidAlgebra.singlestatement · cited by 83
- SkewMonoidAlgebra.coeff_mul_single_auxproof · cited by 2
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