Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_one
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (n : σ →₀ ℕ) [inst_1 : DecidableEq σ],
(MvPowerSeries.coeff n) 1 = if n = 0 then 1 else 0- Defined in
- Mathlib.RingTheory.MvPowerSeries.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Finsuppstatement and proof · cited by 5,255
- MvPowerSeriesstatement · cited by 659
- MvPowerSeries.coeffstatement · cited by 273
- MvPowerSeries.coeff_monomialproof · cited by 17
Cited by5
Results whose statement or proof uses this declaration.
- MvPowerSeries.mul_invOfUnitproof · cited by 4
- MvPowerSeries.coeff_prodproof · cited by 3
- MvPowerSeries.pderiv_X_selfproof · cited by 2
- MvPowerSeries.subst_zero_eq_C_constantCoeffproof · cited by 2
- MvPowerSeries.finSuccEquiv_X_zeroproof · cited by 0