Theorems · Theorem · real analysis
Real.two_mul_arctan
∀ {x : ℝ}, -1 < x → x < 1 → 2 * Real.arctan x = Real.arctan (2 * x / (1 - x ^ 2))- Cited by
- 3 results in Mathlib
- Foundations
- Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- lt_of_not_geproof · cited by 374
- two_mulproof · cited by 232
- Real.arctanstatement and proof · cited by 111
- mul_pos_of_neg_of_negproof · cited by 40
- Real.arctan_addproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Real.two_mul_arctan_inv_3_add_arctan_inv_7proof · cited by 0
- Real.four_mul_arctan_inv_5_sub_arctan_inv_239proof · cited by 0
- Real.two_mul_arctan_inv_2_sub_arctan_inv_7proof · cited by 0