Theorems · Theorem · commutative algebra
PowerSeries.subst_toMvPowerSeries
∀ {σ : Type u_2} {τ : Type u_3} {R : Type u_4} [inst : CommRing R] {f : PowerSeries R} {i : σ}
{a : σ → MvPowerSeries τ R},
MvPowerSeries.HasSubst a → MvPowerSeries.subst a ((PowerSeries.toMvPowerSeries i) f) = PowerSeries.subst (a i) f- Defined in
- Mathlib.RingTheory.MvPowerSeries.Equiv
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- AlgHomstatement · cited by 3,236
- PowerSeriesstatement and proof · cited by 797
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.Xproof · cited by 98
- MvPowerSeries.HasSubststatement and proof · cited by 74
- MvPowerSeries.subststatement and proof · cited by 73
- PowerSeries.subststatement and proof · cited by 58
- PowerSeries.HasSubst.constproof · cited by 15
- PowerSeries.toMvPowerSeriesstatement · cited by 11
- MvPowerSeries.subst_comp_subst_applyproof · cited by 10
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