Theorems · Theorem · real analysis
Real.sqrtTwoAddSeries_step_down
∀ (a b : ℕ) {c d n : ℕ} {z : ℝ},
z ≤ (↑a / ↑b).sqrtTwoAddSeries n →
0 < b → 0 < d → a ^ 2 * d ≤ (2 * d + c) * b ^ 2 → z ≤ (↑c / ↑d).sqrtTwoAddSeries (n + 1)- Defined in
- Mathlib.Analysis.Real.Pi.Bounds
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Real.sqrtTwoAddSeriesstatement and proof · cited by 19
- div_le_div_iff₀proof · cited by 11
- Real.le_sqrt_of_sq_leproof · cited by 10
- add_div_eq_mul_add_divproof · cited by 3
- Real.sqrtTwoAddSeries_monotone_leftproof · cited by 2
- Real.sqrtTwoAddSeries_succproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Real.pi_lt_fourproof · cited by 2
- Real.pi_lt_d2proof · cited by 1
- Real.pi_lt_d20proof · cited by 0
- Real.pi_lt_d4proof · cited by 0
- Real.pi_lt_d6proof · cited by 0