Theorems · Theorem · commutative algebra

MvPowerSeries.coeff_truncTotal_mul_truncTotal_eq_coeff_mul

∀ {σ : Type u_1} {R : Type u_2} {n : ℕ} [inst : Finite σ] [inst_1 : CommSemiring R] (p q : MvPowerSeries σ R)
  {x : σ →₀ ℕ},
  Finsupp.degree x < n →
    MvPolynomial.coeff x ((MvPowerSeries.truncTotal n) p * (MvPowerSeries.truncTotal n) q) =
      (MvPowerSeries.coeff x) (p * q)

Defined in: Mathlib.RingTheory.MvPowerSeries.Trunc
Cited by: 1 results in Mathlib
Foundations: Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Finite CommSemiring

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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
CommSemiringstatement and proof · cited by 10,911
LinearMapstatement · cited by 10,215
Finsuppstatement and proof · cited by 5,255
AddMonoidHomstatement · cited by 3,230
Finitestatement and proof · cited by 3,029
MvPolynomialstatement · cited by 2,140
MvPowerSeriesstatement and proof · cited by 659
MvPolynomial.coeffstatement · cited by 315
MvPowerSeries.coeffstatement · cited by 273
Set.Finite.coe_toFinsetproof · cited by 124

Cited by1

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MvPowerSeries.truncTotal_mul_sub_mul_truncTotal_mem_pow_idealOfVarsproof · cited by 0