Theorems · Theorem · complex analysis
AnalyticWithinAt.im_ofReal
∀ {f : ℂ → ℂ} {s : Set ℝ} {x : ℝ},
AnalyticWithinAt ℂ f (Complex.ofReal '' s) ↑x → AnalyticWithinAt ℝ (fun x => (f ↑x).im) s x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
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
- Realstatement and proof · cited by 25,697
- Set.imagestatement and proof · cited by 5,609
- Complexstatement and proof · cited by 5,565
- Complex.ofRealstatement and proof · cited by 1,654
- Complex.imstatement · cited by 591
- AnalyticWithinAtstatement and proof · cited by 96
- Set.mapsTo_imageproof · cited by 71
- Complex.ofRealCLMproof · cited by 39
- Complex.imCLMproof · cited by 17
- AnalyticWithinAt.compproof · cited by 9
- AnalyticWithinAt.restrictScalarsproof · cited by 3
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