Theorems · Theorem · commutative algebra
PowerSeries.substAlgHom_eq_aeval
∀ {R : Type u_2} [inst : CommRing R] {τ : Type u_3} {S : Type u_4} [inst_1 : CommRing S] [inst_2 : Algebra R S]
{a : MvPowerSeries τ S} [inst_3 : UniformSpace R] [inst_4 : DiscreteUniformity R] [inst_5 : UniformSpace S]
[inst_6 : DiscreteUniformity S] (ha : PowerSeries.HasSubst a), PowerSeries.substAlgHom ha = PowerSeries.aeval ⋯Rewrite PowerSeries.substAlgHom as PowerSeries.aeval.
Its use is discouraged because it introduces a topology and might lead
into awkward comparisons.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- AlgHomstatement · cited by 3,236
- UniformSpacestatement and proof · cited by 2,040
- MulOppositestatement · cited by 1,135
- PowerSeriesstatement and proof · cited by 797
- MvPowerSeriesstatement and proof · cited by 659
- AlgHom.extproof · cited by 170
- PowerSeries.HasSubststatement and proof · cited by 67
- DiscreteUniformitystatement and proof · cited by 25
- MvPowerSeries.substAlgHom_applyproof · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- PowerSeries.summable_substproof · cited by 0
- PowerSeries.subst_tsumproof · cited by 0