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Theorems · Theorem · commutative algebra

MvPowerSeries.HasSubst.const_coeff

∀ {σ : Type u_1} {τ : Type u_4} {S : Type u_5} [inst : CommRing S] {a : σ → MvPowerSeries τ S},
  MvPowerSeries.HasSubst a → ∀ (s : σ), IsNilpotent (MvPowerSeries.constantCoeff (a s))
Defined in
Mathlib.RingTheory.MvPowerSeries.Substitution
Cited by
5 results in Mathlib
Foundations
Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRing
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Around this declaration

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

PowerSeries.hasSubst_iff · cited by 6PowerSeries.hasSubst_iffMvPowerSeries.HasSubst.comp · cited by 4HasSubst.compMvPowerSeries.HasSubst.truncTotal · cited by 3HasSubst.truncTotalMvPowerSeries.IsNilpotent_subst · cited by 1MvPowerSeries.IsNilpotent…MvPowerSeries.HasSubst.map · cited by 1HasSubst.mapDFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingRingHom · cited by 10189RingHomMvPowerSeries · cited by 659MvPowerSeriesIsNilpotent · cited by 248IsNilpotentMvPowerSeries.constantCoeff · cited by 98MvPowerSeries.constantCoe…MvPowerSeries.HasSubst · cited by 74MvPowerSeries.HasSubstHasSubst.const_coeffCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.