Theorems · Theorem · real analysis
Real.arctan_add
∀ {x y : ℝ}, x * y < 1 → Real.arctan x + Real.arctan y = Real.arctan ((x + y) / (1 - x * y))- Cited by
- 6 results in Mathlib
- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.piproof · cited by 1,774
- Real.arctanstatement and proof · cited by 111
- Real.tanproof · cited by 100
- neg_addproof · cited by 69
- neg_mul_negproof · cited by 32
- neg_ltproof · cited by 21
- Real.tan_arctanproof · cited by 11
- Real.arctan_negproof · cited by 6
- Real.arctan_tanproof · cited by 4
- Real.tan_add'proof · cited by 1
- Real.arctan_ne_mul_pi_div_twoproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- Real.two_mul_arctanproof · cited by 3
- Real.arctan_add_eq_add_piproof · cited by 2
- Real.four_mul_arctan_inv_5_sub_arctan_inv_239proof · cited by 0
- Real.arctan_inv_2_add_arctan_inv_3proof · cited by 0
- Real.two_mul_arctan_inv_2_sub_arctan_inv_7proof · cited by 0
- Real.two_mul_arctan_inv_3_add_arctan_inv_7proof · cited by 0