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Theorems · Theorem · several complex variables

AnalyticAt.neg

∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} {F : Type u_4} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F} {x : E},
  AnalyticAt 𝕜 f x → AnalyticAt 𝕜 (-f) x
Defined in
Mathlib.Analysis.Analytic.Constructions
Cited by
8 results in Mathlib
Foundations
Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AnalyticAt.sub · cited by 9AnalyticAt.subAnalyticAt.harmonicAt_log_norm · cited by 4AnalyticAt.harmonicAt_log…meromorphicTrailingCoeffAt_neg · cited by 2meromorphicTrailingCoeffA…UpperHalfPlane.qExpansion_sub · cited by 1UpperHalfPlane.qExpansion…AnalyticAt.fun_neg · cited by 1AnalyticAt.fun_neganalyticOrderAt_neg · cited by 1analyticOrderAt_neganalyticAt_neg · cited by 1analyticAt_negAnalyticOnNhd.neg · cited by 0AnalyticOnNhd.negNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldFormalMultilinearSeries · cited by 615FormalMultilinearSeriesAnalyticAt · cited by 321AnalyticAtHasFPowerSeriesAt · cited by 94HasFPowerSeriesAtHasFPowerSeriesAt.analyticAt · cited by 11HasFPowerSeriesAt.analyti…HasFPowerSeriesAt.neg · cited by 2HasFPowerSeriesAt.negAnalyticAt.negCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by8

Results whose statement or proof uses this declaration.