Theorems · Theorem · real analysis
Real.arctan_add_arctan_lt_pi_div_two
∀ {x y : ℝ}, x * y < 1 → Real.arctan x + Real.arctan y < Real.pi / 2- Cited by
- 1 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- add_zeroproof · cited by 2,707
- Real.pistatement and proof · cited by 1,774
- OrderIso.symmproof · cited by 475
- le_or_gtproof · cited by 269
- Real.arctanstatement and proof · cited by 111
- lt_div_iff₀proof · cited by 44
- add_lt_add_of_lt_of_leproof · cited by 37
- inv_eq_one_divproof · cited by 33
- OrderIso.strictMonoproof · cited by 26
- OrderIso.monotoneproof · cited by 23
- Real.arctan_zeroproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Real.arctan_addproof · cited by 6