Theorems · Theorem · commutative algebra
PowerSeries.coeff_zero_eq_constantCoeff
∀ {R : Type u_1} [inst : Semiring R], ⇑(PowerSeries.coeff 0) = ⇑PowerSeries.constantCoeff- Defined in
- Mathlib.RingTheory.PowerSeries.Basic
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 95 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.
Cites11
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 and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement · cited by 10,189
- Finsuppproof · cited by 5,255
- PowerSeriesstatement and proof · cited by 797
- PowerSeries.coeffstatement · cited by 324
- MvPowerSeries.coeffproof · cited by 273
- PowerSeries.constantCoeffstatement and proof · cited by 126
- Finsupp.single_zeroproof · cited by 63
Cited by41
Results whose statement or proof uses this declaration.
- PowerSeries.coeff_zero_eq_constantCoeff_applyproof · cited by 8
- PowerSeries.rescale_zeroproof · cited by 3
- PowerSeries.eq_X_mul_shift_add_constproof · cited by 2
- EisensteinSeries.E_qExpansion_coeff_zeroproof · cited by 2
- PowerSeries.eq_shift_mul_X_add_constproof · cited by 2
- HahnSeries.SummableFamily.powerSeriesFamily_of_not_orderTop_posproof · cited by 2
- PowerSeries.mk_one_mul_one_sub_eq_oneproof · cited by 2
- PowerSeries.one_le_order_iff_constCoeff_eq_zeroproof · cited by 2
- PowerSeries.trunc_one_leftproof · cited by 2
- Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_mapproof · cited by 2
- PowerSeries.IsWeierstrassDivision.isUnit_of_map_ne_zeroproof · cited by 2
- Polynomial.IsDistinguishedAt.map_ne_zero_of_eq_mulproof · cited by 2