Theorems · Theorem · commutative algebra
PowerSeries.IsWeierstrassDivisorAt.mod.congr_simp
∀ {A : Type u_1} [inst : CommRing A] {g g_1 : PowerSeries A} (e_g : g = g_1) {I I_1 : Ideal A} (e_I : I = I_1)
(H : g.IsWeierstrassDivisorAt I) (f f_1 : PowerSeries A),
f = f_1 → ∀ [inst_1 : IsPrecomplete I A], H.mod f = ⋯.mod f_1- 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.
Cites7
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
- Polynomialstatement · cited by 5,681
- Idealstatement and proof · cited by 4,748
- PowerSeriesstatement and proof · cited by 797
- IsPrecompletestatement and proof · cited by 29
- PowerSeries.IsWeierstrassDivisorAtstatement and proof · cited by 28
- PowerSeries.IsWeierstrassDivisorAt.modstatement and proof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassDivisorAt.mod_zeroproof · cited by 1