Theorems · Theorem · commutative algebra
PowerSeries.coeff_one
∀ {R : Type u_1} [inst : Semiring R] (n : ℕ), (PowerSeries.coeff n) 1 = if n = 0 then 1 else 0- Defined in
- Mathlib.RingTheory.PowerSeries.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 98 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.
Cites7
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
- PowerSeriesstatement · cited by 797
- PowerSeries.coeffstatement · cited by 324
- PowerSeries.coeff_Cproof · cited by 11
Cited by17
Results whose statement or proof uses this declaration.
- sum_range_powproof · cited by 2
- bernoulli'_eq_zero_of_oddproof · cited by 2
- UpperHalfPlane.qExpansion_oneproof · cited by 2
- PowerSeries.mk_one_mul_one_sub_eq_oneproof · cited by 2
- PowerSeries.divXPowOrder_Xproof · cited by 1
- FormalGroup.coeff_one_Xzeroproof · cited by 1
- FormalGroup.coeff_one_zeroXproof · cited by 1
- bernoulli'PowerSeries_mul_exp_sub_oneproof · cited by 1
- PowerSeries.invUnitsSub_mul_Xproof · cited by 1
- bernoulliPowerSeries_mul_exp_sub_oneproof · cited by 1
- PowerSeries.coeff_subst_sum_C_substInvFun_mul_X_pow_sub_Xproof · cited by 1
- PowerSeries.divXPowOrder_oneproof · cited by 0