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Theorems · Theorem · several complex variables

AnalyticOnNhd.mono

∀ {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] {f : E → F} {s t : Set E},
  AnalyticOnNhd 𝕜 f t → s ⊆ t → AnalyticOnNhd 𝕜 f s
Defined in
Mathlib.Analysis.Analytic.Basic
Cited by
8 results in Mathlib
Foundations
Depth 167 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.

MeromorphicOn.circleIntegrable_log_norm · cited by 11MeromorphicOn.circleInteg…MeromorphicOn.circleAverage_log_norm · cited by 3MeromorphicOn.circleAvera…AnalyticOn.hasFPowerSeriesOnSubball · cited by 2AnalyticOn.hasFPowerSerie…InnerProductSpace.HarmonicOnNhd.circleAverage_re_herglotzRieszKernel_smul · cited by 2HarmonicOnNhd.circleAvera…AnalyticOnNhd.comp · cited by 2AnalyticOnNhd.compAnalyticWithinAt.exists_hasFTaylorSeriesUpToOn · cited by 1AnalyticWithinAt.exists_h…ContDiff.analyticOnNhd · cited by 1ContDiff.analyticOnNhdAnalyticOnNhd.sum_divisor_le · cited by 0AnalyticOnNhd.sum_divisor…Set · cited by 53352SetNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldAnalyticOnNhd · cited by 206AnalyticOnNhdAnalyticOnNhd.monoCITED BYCITES

Cites5

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Cited by8

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