Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_C_mul
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R),
(MvPowerSeries.coeff n) (MvPowerSeries.C a * φ) = a * (MvPowerSeries.coeff n) φ- Defined in
- Mathlib.RingTheory.MvPowerSeries.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Finsuppstatement and proof · cited by 5,255
- zero_addproof · cited by 2,366
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffstatement and proof · cited by 273
- MvPowerSeries.Cstatement and proof · cited by 62
- MvPowerSeries.coeff_add_monomial_mulproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- PowerSeries.coeff_C_mulproof · cited by 8
- MvPowerSeries.smul_eq_C_mulproof · cited by 4
- MvPowerSeries.trunc'_C_mulproof · cited by 0
- MvPowerSeries.trunc_C_mulproof · cited by 0