Theorems · Theorem · real analysis
Real.cos_arctan_pos
∀ (x : ℝ), 0 < Real.cos (Real.arctan x)
- Cited by
- 6 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Real.cosstatement · cited by 424
- Real.arctanstatement · cited by 111
- Real.cos_pos_of_mem_Iooproof · cited by 14
- Real.arctan_mem_Iooproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- Real.contDiff_arctanproof · cited by 4
- Real.hasStrictDerivAt_arctanproof · cited by 3
- Real.sin_arctanproof · cited by 1
- Real.cos_sq_arctanproof · cited by 1
- Real.cos_arctanproof · cited by 1
- Real.sin_sq_arctanproof · cited by 0