Theorems · Theorem · commutative algebra
MvPowerSeries.hasSum_aeval
∀ {σ : Type u_1} {R : Type u_2} [inst : CommRing R] [inst_1 : UniformSpace R] {S : Type u_3} [inst_2 : CommRing S]
[inst_3 : UniformSpace S] {a : σ → S} [inst_4 : IsTopologicalSemiring R] [inst_5 : IsUniformAddGroup R]
[inst_6 : IsUniformAddGroup S] [inst_7 : CompleteSpace S] [inst_8 : T2Space S] [inst_9 : IsTopologicalRing S]
[inst_10 : IsLinearTopology S S] [inst_11 : Algebra R S] [inst_12 : ContinuousSMul R S] (ha : MvPowerSeries.HasEval a)
(f : MvPowerSeries σ R),
HasSum (fun d => (MvPowerSeries.coeff d) f • d.prod fun s e => a s ^ e) ((MvPowerSeries.aeval ha) f)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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Cited by3
Results whose statement or proof uses this declaration.
- MvPowerSeries.coeff_substproof · cited by 15
- MvPowerSeries.coeff_subst_finiteproof · cited by 6
- MvPowerSeries.aeval_eq_sumproof · cited by 0