Theorems · Theorem · complex analysis
FormalMultilinearSeries.ofScalarsSum_zero
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Field 𝕜] [inst_1 : Ring E] [inst_2 : Algebra 𝕜 E] [inst_3 : TopologicalSpace E]
[inst_4 : IsTopologicalRing E] (c : ℕ → 𝕜), FormalMultilinearSeries.ofScalarsSum c 0 = c 0 • 1- Defined in
- Mathlib.Analysis.Analytic.OfScalars
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- SummationFilter.unconditionalproof · cited by 2,068
- tsumproof · cited by 1,148
- IsTopologicalRingstatement and proof · cited by 402
- FormalMultilinearSeries.ofScalarsSumstatement · cited by 8
- tsum_pi_singleproof · cited by 3
- FormalMultilinearSeries.ofScalarsSum_eq_tsumproof · cited by 2
- FormalMultilinearSeries.ofScalars_apply_zeroproof · cited by 1
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