Theorems · Theorem · real analysis
Real.pi_lt_sqrtTwoAddSeries
∀ (n : ℕ), Real.pi < 2 ^ (n + 1) * √(2 - Real.sqrtTwoAddSeries 0 n) + 1 / 4 ^ n
- Defined in
- Mathlib.Analysis.Real.Pi.Bounds
- 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.
Cites32
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
- mul_commproof · cited by 2,262
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- add_commproof · cited by 1,535
- le_of_ltproof · cited by 1,175
- add_assocproof · cited by 746
- one_divproof · cited by 624
- Real.sqrtstatement and proof · cited by 545
- lt_of_lt_of_leproof · cited by 438
- le_of_eqproof · cited by 366
Cited by1
Results whose statement or proof uses this declaration.
- Real.pi_upper_bound_startproof · cited by 5