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Theorems · Theorem · commutative algebra

MvPowerSeries.continuous_subst

∀ {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 →
    ∀ [inst_3 : UniformSpace R] [DiscreteUniformity R] [inst_5 : UniformSpace S] [DiscreteUniformity S],
      Continuous (MvPowerSeries.subst a)
Defined in
Mathlib.RingTheory.MvPowerSeries.Substitution
Cited by
2 results in Mathlib
Foundations
Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraUniformSpaceDiscreteUniformityUniformSpaceDiscreteUniformity
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Around this declaration

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

MvPowerSeries.HasSubst.comp · cited by 4HasSubst.compMvPowerSeries.substAlgHom_comp_substAlgHom · cited by 3MvPowerSeries.substAlgHom…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraContinuous · cited by 2592ContinuousUniformSpace · cited by 2040UniformSpaceMvPowerSeries · cited by 659MvPowerSeriesMvPowerSeries.HasSubst · cited by 74MvPowerSeries.HasSubstMvPowerSeries.subst · cited by 73MvPowerSeries.substcontinuous_algebraMap · cited by 29continuous_algebraMapDiscreteUniformity · cited by 25DiscreteUniformityMvPowerSeries.HasSubst.hasEval · cited by 14HasSubst.hasEvalMvPowerSeries.continuous_eval₂ · cited by 4MvPowerSeries.continuous_…MvPowerSeries.subst_eq_eval₂ · cited by 3MvPowerSeries.subst_eq_ev…MvPowerSeries.continuous_substCITED BYCITES

Cites12

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Cited by2

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