Theorems · Theorem · several complex variables
FormalMultilinearSeries.sum_of_finite
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
(p : FormalMultilinearSeries 𝕜 E F) {n : ℕ}, (∀ (m : ℕ), n ≤ m → p m = 0) → ∀ (x : E), p.sum x = p.partialSum n x- Defined in
- Mathlib.Analysis.Analytic.CPolynomialDef
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Finset.rangeproof · cited by 1,341
- ContinuousMultilinearMapstatement and proof · cited by 1,016
- FormalMultilinearSeriesstatement and proof · cited by 615
- not_ltproof · cited by 306
- Finset.mem_rangeproof · cited by 140
- FormalMultilinearSeries.sumstatement · cited by 34
- FormalMultilinearSeries.partialSumstatement · cited by 30
- tsum_eq_sumproof · cited by 11
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