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Theorems · Theorem · complex analysis

analyticAt_fst

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {p : E × F},
  AnalyticAt 𝕜 (fun p => p.1) p

fst is analytic

Defined in
Mathlib.Analysis.Analytic.Linear
Cited by
2 results in Mathlib
Foundations
Depth 186 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.

analyticWithinAt_fst · cited by 1analyticWithinAt_fstanalyticOnNhd_fst · cited by 0analyticOnNhd_fstNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldAnalyticAt · cited by 321AnalyticAtContinuousLinearMap.fst · cited by 86ContinuousLinearMap.fstContinuousLinearMap.analyticAt · cited by 14ContinuousLinearMap.analy…analyticAt_fstCITED BYCITES

Cites6

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

Cited by2

Results whose statement or proof uses this declaration.