Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_truncTotal_eq_zero
∀ {σ : Type u_1} {R : Type u_2} {n : ℕ} [inst : Finite σ] [inst_1 : CommSemiring R] (p : MvPowerSeries σ R)
{x : σ →₀ ℕ}, n ≤ Finsupp.degree x → MvPolynomial.coeff x ((MvPowerSeries.truncTotal n) p) = 0- Defined in
- Mathlib.RingTheory.MvPowerSeries.Trunc
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FiniteCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Finsupp.degreestatement and proof · cited by 94
- MvPowerSeries.truncTotalstatement · cited by 28
Cited by4
Results whose statement or proof uses this declaration.
- MvPowerSeries.coeff_truncTotal_eq_iteproof · cited by 3
- MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_sumproof · cited by 2
- MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_truncTotal_of_leproof · cited by 1
- MvPowerSeries.truncTotal_pow_eq_truncTotal_truncTotal_powproof · cited by 0