Theorems · Theorem · commutative algebra
PowerSeries.coeff_succ_X_mul
∀ {R : Type u_1} [inst : Semiring R] (n : ℕ) (φ : PowerSeries R),
(PowerSeries.coeff (n + 1)) (PowerSeries.X * φ) = (PowerSeries.coeff n) φ- Defined in
- Mathlib.RingTheory.PowerSeries.Basic
- Cited by
- 4 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.
Cites15
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
- one_mulproof · cited by 2,841
- add_commproof · cited by 1,535
- 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
Cited by4
Results whose statement or proof uses this declaration.
- PowerSeries.eq_X_mul_shift_add_constproof · cited by 2
- PowerSeries.mk_one_mul_one_sub_eq_oneproof · cited by 2
- PowerSeries.X_mul_cancelproof · cited by 1
- Polynomial.bernoulli_generating_functionproof · cited by 0