Theorems · Theorem · real analysis
Real.arctan_mem_Ioo
∀ (x : ℝ), Real.arctan x ∈ Set.Ioo (-(Real.pi / 2)) (Real.pi / 2)
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Real.pistatement · cited by 1,774
- Set.Ioostatement · cited by 1,214
- OrderIso.symmproof · cited by 475
- Real.arctanstatement · cited by 111
- Subtype.coe_propproof · cited by 42
- Real.tanOrderIsoproof · cited by 10
Cited by8
Results whose statement or proof uses this declaration.
- Real.cos_arctan_posproof · cited by 6
- Real.sin_arctan_strictMonoproof · cited by 5
- Real.arctan_eq_arcsinproof · cited by 5
- Real.tanPartialHomeomorphproof · cited by 4
- Real.arctan_lt_pi_div_twoproof · cited by 3
- Real.arctan_eq_of_tan_eqproof · cited by 2
- Real.arctan_ne_mul_pi_div_twoproof · cited by 1
- Real.neg_pi_div_two_lt_arctanproof · cited by 1