Theorems · Theorem · several complex variables
AnalyticOnNhd.congr
∀ {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 g : E → F} {s : Set E},
IsOpen s → AnalyticOnNhd 𝕜 f s → Set.EqOn f g s → AnalyticOnNhd 𝕜 g s- Defined in
- Mathlib.Analysis.Analytic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- IsOpenstatement and proof · cited by 2,400
- Set.EqOnstatement and proof · cited by 603
- IsOpen.mem_nhdsproof · cited by 470
- AnalyticOnNhdstatement and proof · cited by 206
- Filter.eventuallyEq_iff_exists_memproof · cited by 19
- mem_nhdsSet_iff_forallproof · cited by 12
- AnalyticOnNhd.congr'proof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- analyticOnNhd_congrproof · cited by 0