Mathlib Map

Theorems · Theorem · commutative algebra

PowerSeries.weierstrassMod.congr_simp

∀ {A : Type u_1} [inst : CommRing A] [inst_1 : IsLocalRing A] (f f_1 : PowerSeries A),
  f = f_1 →
    ∀ (g g_1 : PowerSeries A), g = g_1 → ∀ [inst_2 : IsPrecomplete (IsLocalRing.maximalIdeal A) A], f %ʷ g = f_1 %ʷ g_1
Defined in
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation
Cited by
0 results in Mathlib
Foundations
Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingIsLocalRingIsPrecomplete
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CommRing · cited by 17173CommRingPolynomial · cited by 5681PolynomialPowerSeries · cited by 797PowerSeriesIsLocalRing · cited by 339IsLocalRingIsLocalRing.maximalIdeal · cited by 297IsLocalRing.maximalIdealIsPrecomplete · cited by 29IsPrecompletePowerSeries.weierstrassMod · cited by 11PowerSeries.weierstrassModweierstrassMod.congr_simpCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.