Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_truncFinset_of_mem
∀ {σ : Type u_1} {R : Type u_2} [inst : CommSemiring R] {s : Finset (σ →₀ ℕ)} {x : σ →₀ ℕ} (p : MvPowerSeries σ R),
x ∈ s → MvPolynomial.coeff x ((MvPowerSeries.truncFinset R s) p) = (MvPowerSeries.coeff x) p- Defined in
- Mathlib.RingTheory.MvPowerSeries.Trunc
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- Finset.sum_congrproof · cited by 2,323
- MvPolynomialstatement · cited by 2,140
- MvPowerSeriesstatement and proof · cited by 659
- MvPolynomial.coeffstatement and proof · cited by 315
- MvPowerSeries.coeffstatement and proof · cited by 273
- MvPolynomial.monomialproof · cited by 253
Cited by3
Results whose statement or proof uses this declaration.
- MvPowerSeries.coeff_truncTotalproof · cited by 10
- MvPowerSeries.coeff_truncFinset_mul_truncFinset_eq_coeff_mul₂proof · cited by 3
- MvPowerSeries.truncFinset_truncFinset_powproof · cited by 1