Theorems · Theorem · commutative algebra
PowerSeries.coeff_succ_mul_X
∀ {R : Type u_1} [inst : Semiring R] (n : ℕ) (φ : PowerSeries R),
(PowerSeries.coeff (n + 1)) (φ * PowerSeries.X) = (PowerSeries.coeff n) φ- Defined in
- Mathlib.RingTheory.PowerSeries.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 90 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.
Cites14
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
- mul_oneproof · cited by 3,885
- Finsupp.singleproof · cited by 943
- PowerSeriesstatement and proof · cited by 797
- DFunLikeproof · cited by 576
- PowerSeries.coeffstatement · cited by 324
- MvPowerSeries.coeffproof · cited by 273
- PowerSeries.Xstatement and proof · cited by 183
- MvPowerSeries.monomialproof · cited by 69
Cited by6
Results whose statement or proof uses this declaration.
- PowerSeries.eq_shift_mul_X_add_constproof · cited by 2
- PowerSeries.coeff_subst_sum_C_substInvFun_mul_X_pow_sub_Xproof · cited by 1
- bernoulli'PowerSeries_mul_exp_sub_oneproof · cited by 1
- PowerSeries.mul_X_cancelproof · cited by 1
- PowerSeries.invUnitsSub_mul_Xproof · cited by 1
- PowerSeries.catalanSeries_sq_mul_X_add_oneproof · cited by 0