Theorems · Theorem · commutative algebra
PowerSeries.IsWeierstrassDivisorAt.div_smul
∀ {A : Type u_1} [inst : CommRing A] {g : PowerSeries A} {I : Ideal A} (H : g.IsWeierstrassDivisorAt I) (a : A)
(f : PowerSeries A) [inst_1 : IsAdicComplete I A], H.div (a • f) = a • H.div f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsAdicComplete
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- PowerSeriesstatement and proof · cited by 797
- IsAdicCompletestatement and proof · cited by 124
- PowerSeries.IsWeierstrassDivisorAtstatement and proof · cited by 28
- PowerSeries.IsWeierstrassDivisorAt.divstatement and proof · cited by 18
- PowerSeries.IsWeierstrassDivisorAt.modproof · cited by 16
- PowerSeries.IsWeierstrassDivisionAtproof · cited by 12
- PowerSeries.IsWeierstrassDivisionAt.eq_mul_addproof · cited by 11
- PowerSeries.IsWeierstrassDivisorAt.isWeierstrassDivisionAt_div_modproof · cited by 10
- PowerSeries.IsWeierstrassDivisionAt.degree_ltproof · cited by 8
- PowerSeries.IsWeierstrassDivisorAt.eq_of_mul_add_eq_mul_addproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassDivisorAt.div_zeroproof · cited by 1
- PowerSeries.smul_weierstrassDivproof · cited by 0