Theorems · Theorem · complex analysis
Real.exp_approx_succ
∀ {n : ℕ} {x a₁ b₁ : ℝ} (m : ℕ),
n + 1 = m →
∀ (a₂ b₂ : ℝ),
|1 + x / ↑m * a₂ - a₁| ≤ b₁ - |x| / ↑m * b₂ →
|Real.exp x - Real.expNear m x a₂| ≤ |x| ^ m / ↑m.factorial * b₂ →
|Real.exp x - Real.expNear n x a₁| ≤ |x| ^ n / ↑n.factorial * b₁- Defined in
- Mathlib.Analysis.Complex.Exponential
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- le_reflproof · cited by 2,061
- absstatement and proof · cited by 1,814
- Real.expstatement and proof · cited by 871
- div_eq_mul_invproof · cited by 715
- add_le_addproof · cited by 666
- Nat.factorialstatement and proof · cited by 616
- Nat.cast_addproof · cited by 586
- le_imp_le_of_le_of_leproof · cited by 576
- mul_addproof · cited by 413
- mul_le_mul_of_nonneg_leftproof · cited by 361
Cited by2
Results whose statement or proof uses this declaration.
- Real.exp_1_approx_succ_eqproof · cited by 2
- Real.exp_approx_end'proof · cited by 2