Theorems · Theorem · commutative algebra

MvPowerSeries.constantCoeff_subst_eq_zero

∀ {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},
  MvPowerSeries.HasSubst a →
    (∀ (i : σ), MvPowerSeries.constantCoeff (a i) = 0) →
      ∀ {f : MvPowerSeries σ R},
        MvPowerSeries.constantCoeff f = 0 → MvPowerSeries.constantCoeff (MvPowerSeries.subst a f) = 0

Defined in

Mathlib.RingTheory.MvPowerSeries.Substitution

Cited by

7 results in Mathlib

Foundations

Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra