Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_zero_eq_constantCoeff_apply
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (φ : MvPowerSeries σ R),
(MvPowerSeries.coeff 0) φ = MvPowerSeries.constantCoeff φ- Defined in
- Mathlib.RingTheory.MvPowerSeries.Basic
- Cited by
- 7 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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 · cited by 5,255
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffstatement · cited by 273
- MvPowerSeries.constantCoeffstatement · cited by 98
Cited by7
Results whose statement or proof uses this declaration.
- MvPowerSeries.mul_invOfUnitproof · cited by 4
- MvPowerSeries.HasSubst.truncTotalproof · cited by 3
- MvPowerSeries.constantCoeff_invproof · cited by 2
- MvPowerSeries.constantCoeff_invOfUnitproof · cited by 2
- MvPowerSeries.truncTotal_subst_eq_truncTotal_sum_subst_truncTotal_of_leproof · cited by 2
- MvPowerSeries.constantCoeff_renameproof · cited by 1
- PowerSeries.subst_rescale_of_degree_eq_oneproof · cited by 0