Theorems · Theorem · commutative algebra

MvPowerSeries.subst_comp_subst_apply

∀ {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} {υ : Type u_7} {T : Type u_8} [inst_3 : CommRing T]
  [inst_4 : Algebra R T] [inst_5 : Algebra S T] [IsScalarTower R S T] {b : τ → MvPowerSeries υ T},
  MvPowerSeries.HasSubst a →
    MvPowerSeries.HasSubst b →
      ∀ (f : MvPowerSeries σ R),
        MvPowerSeries.subst b (MvPowerSeries.subst a f) = MvPowerSeries.subst (fun s => MvPowerSeries.subst b (a s)) f

Defined in

Mathlib.RingTheory.MvPowerSeries.Substitution

Cited by

10 results in Mathlib

Foundations

Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTower