Theorems · Theorem · real analysis
Real.pi_gt_sqrtTwoAddSeries
∀ (n : ℕ), 2 ^ (n + 1) * √(2 - Real.sqrtTwoAddSeries 0 n) < Real.pi
- Defined in
- Mathlib.Analysis.Real.Pi.Bounds
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- mul_commproof · cited by 2,262
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- mul_assocproof · cited by 1,667
- Real.sqrtstatement and proof · cited by 545
- lt_of_le_of_ltproof · cited by 432
- le_of_eqproof · cited by 366
- div_posproof · cited by 337
- pow_posproof · cited by 292
- pow_succ'proof · cited by 228
- Real.pi_posproof · cited by 173
Cited by1
Results whose statement or proof uses this declaration.
- Real.pi_lower_bound_startproof · cited by 5