Theorems · Theorem · real analysis
Real.cos_lt_one_div_sqrt_sq_add_one
∀ {x : ℝ}, -(3 * Real.pi / 2) ≤ x → x ≤ 3 * Real.pi / 2 → x ≠ 0 → Real.cos x < 1 / √(x ^ 2 + 1)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
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
- LT.lt.leproof · cited by 2,189
- Nat.cast_zeroproof · cited by 1,870
- absproof · cited by 1,814
- Real.pistatement and proof · cited by 1,774
- add_commproof · cited by 1,535
- LT.lt.ne'proof · cited by 1,417
- one_divproof · cited by 624
- Real.sqrtstatement and proof · cited by 545
- one_powproof · cited by 521
- inv_invproof · cited by 494
Cited by1
Results whose statement or proof uses this declaration.
- Real.cos_le_one_div_sqrt_sq_add_oneproof · cited by 0