Theorems · Theorem · commutative algebra
PowerSeries.IsWeierstrassDivisorAt.coeff_div_sub_seq_mem
∀ {A : Type u_1} [inst : CommRing A] {g : PowerSeries A} {I : Ideal A} (H : g.IsWeierstrassDivisorAt I)
(f : PowerSeries A) [inst_1 : IsPrecomplete I A] (k i : ℕ), (PowerSeries.coeff i) (H.div f - H.seq f k) ∈ I ^ k- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsPrecomplete
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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 · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Idealstatement and proof · cited by 4,748
- PowerSeriesstatement and proof · cited by 797
- map_subproof · cited by 565
- PowerSeries.coeffstatement and proof · cited by 324
- SModEqproof · cited by 80
- Ideal.mul_topproof · cited by 42
- IsPrecompletestatement and proof · cited by 29
- PowerSeries.IsWeierstrassDivisorAtstatement and proof · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassDivisorAt.isWeierstrassDivisionAt_div_modproof · cited by 10