Theorems · Theorem · commutative algebra

MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_truncTotal_of_le

∀ {σ : Type u_1} {R : Type u_3} [inst : CommRing R] {τ : Type u_4} {S : Type u_5} [inst_1 : CommRing S]
  [inst_2 : Algebra R S] {a : σ → MvPowerSeries τ S} {f : MvPowerSeries σ R} [inst_3 : Finite τ] {x : σ → ℕ} {k : ℕ},
  MvPowerSeries.HasSubst a →
    (∀ (i : σ), k ≤ x i) →
      (MvPowerSeries.truncTotal k) (MvPowerSeries.subst a f) =
        (MvPowerSeries.truncTotal k) (MvPowerSeries.subst (fun i => ↑((MvPowerSeries.truncTotal (x i)) (a i))) f)

Defined in

Mathlib.RingTheory.MvPowerSeries.Substitution

Cited by

1 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFinite