Theorems · Theorem · commutative algebra
PowerSeries.toMvPowerSeries_coeff_eq_zero
∀ {σ : Type u_2} {R : Type u_4} [inst : CommRing R] {f : PowerSeries R} {i : σ} {d : σ →₀ ℕ},
d i = 0 → PowerSeries.constantCoeff f = 0 → (MvPowerSeries.coeff d) ((PowerSeries.toMvPowerSeries i) f) = 0- Defined in
- Mathlib.RingTheory.MvPowerSeries.Equiv
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Finsuppstatement and proof · cited by 5,255
- mul_oneproof · cited by 3,885
- AlgHomstatement · cited by 3,236
- MulZeroClass.mul_zeroproof · cited by 2,091
- Finsupp.singleproof · cited by 943
- PowerSeriesstatement and proof · cited by 797
- MvPowerSeriesstatement and proof · cited by 659
Cited by1
Results whose statement or proof uses this declaration.
- MvPowerSeries.HasSubst.toMvPowerSeriesproof · cited by 0