Theorems · Theorem · several complex variables
AnalyticOn.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},
AnalyticOn 𝕜 f t → s ⊆ t → AnalyticOn 𝕜 f s- Defined in
- Mathlib.Analysis.Analytic.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- AnalyticOnstatement and proof · cited by 161
- AnalyticWithinAt.monoproof · cited by 3
Cited by13
Results whose statement or proof uses this declaration.
- ContDiffWithinAt.compproof · cited by 18
- ContDiffWithinAt.prodMkproof · cited by 17
- ContDiffWithinAt.congr_of_eventuallyEqproof · cited by 9
- ContDiffWithinAt.contDiffOn'proof · cited by 7
- contDiffWithinAt_succ_iff_hasFDerivWithinAtproof · cited by 5
- contDiffWithinAt_piproof · cited by 3
- HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sumproof · cited by 2
- ProbabilityTheory.exists_cgf_eq_iteratedDeriv_two_cgf_mulproof · cited by 1
- contDiffWithinAt_succ_iff_hasFDerivWithinAt'proof · cited by 1
- HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sum_of_completeSpaceproof · cited by 1
- AnalyticWithinAt.exists_hasFTaylorSeriesUpToOnproof · cited by 1
- Real.analyticOn_arcoshproof · cited by 0