Theorems · Theorem · complex analysis
Complex.liouville_theorem_aux
∀ {F : Type v} [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℂ F] {f : ℂ → F},
Differentiable ℂ f → Bornology.IsBounded (Set.range f) → ∀ (z w : ℂ), f z = f wAn auxiliary lemma for Liouville's theorem Differentiable.apply_eq_apply_of_bounded.
- Defined in
- Mathlib.Analysis.Complex.Liouville
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 288 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- Set.rangestatement and proof · cited by 4,705
- LE.le.transproof · cited by 3,151
- LT.lt.ne'proof · cited by 1,417
- derivproof · cited by 676
- zero_lt_oneproof · cited by 598
- Metric.sphereproof · cited by 371
- div_posproof · cited by 337
Cited by1
Results whose statement or proof uses this declaration.
- Differentiable.apply_eq_apply_of_boundedproof · cited by 1