Theorems · Theorem · real analysis
Real.tendsto_abs_tan_of_cos_eq_zero
∀ {x : ℝ}, Real.cos x = 0 → Filter.Tendsto (fun x => |Real.tan x|) (nhdsWithin x {x}ᶜ) Filter.atTop- Cited by
- 2 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Norm.normproof · cited by 5,413
- Filter.Tendstostatement and proof · cited by 3,814
- Compl.complstatement and proof · cited by 2,925
- Filter.atTopstatement and proof · cited by 2,405
- nhdsWithinstatement and proof · cited by 1,912
- Nat.cast_zeroproof · cited by 1,870
- absstatement · cited by 1,814
- Complex.ofRealproof · cited by 1,654
- Filter.Tendsto.compproof · cited by 560
- Real.cosstatement and proof · cited by 424
Cited by2
Results whose statement or proof uses this declaration.
- Real.continuousAt_tanproof · cited by 2
- Real.tendsto_abs_tan_atTopproof · cited by 0