Theorems · Theorem · commutative algebra

PowerSeries.weierstrassDiv.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] (a a_1 : Unit →₀ ℕ),
          a = a_1 → (f /ʷ g) a = (f_1 /ʷ g_1) a_1

Defined in: Mathlib.RingTheory.PowerSeries.WeierstrassPreparation
Cited by: 0 results in Mathlib
Foundations: Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsLocalRing IsPrecomplete

Mathlib docs Source Loogle LeanSearch

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
Finsuppstatement and proof · cited by 5,255
PowerSeriesstatement and proof · cited by 797
IsLocalRingstatement and proof · cited by 339
IsLocalRing.maximalIdealstatement and proof · cited by 297
IsPrecompletestatement and proof · cited by 29
PowerSeries.weierstrassDivstatement and proof · cited by 10

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.