Theorems · Theorem · real analysis
Real.tan_arctan
∀ (x : ℝ), Real.tan (Real.arctan x) = x
- Cited by
- 11 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.
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.arctanstatement · cited by 111
- Real.tanstatement · cited by 100
- OrderIso.apply_symm_applyproof · cited by 45
- Real.tanOrderIsoproof · cited by 10
Cited by12
Results whose statement or proof uses this declaration.
- Real.arctan_addproof · cited by 6
- InnerProductGeometry.tan_angle_add_of_inner_eq_zeroproof · cited by 5
- Real.tanPartialHomeomorphproof · cited by 4
- Real.arctan_inv_of_posproof · cited by 3
- Real.arctan_eq_of_tan_eqproof · cited by 2
- Orientation.tan_oangle_add_right_smul_rotation_pi_div_twoproof · cited by 1
- Real.cos_sq_arctanproof · cited by 1
- Real.cos_arctanproof · cited by 1
- Real.sin_arctanproof · cited by 1
- Orientation.tan_oangle_add_left_smul_rotation_pi_div_twoproof · cited by 0
- Real.sin_sq_arctanproof · cited by 0
- Complex.ofReal_arctanproof · cited by 0