Theorems · Theorem · complex analysis
Real.exp_1_approx_succ_eq
∀ {n : ℕ} {a₁ b₁ : ℝ} {m : ℕ},
n + 1 = m →
∀ {rm : ℝ},
↑m = rm →
|Real.exp 1 - Real.expNear m 1 ((a₁ - 1) * rm)| ≤ |1| ^ m / ↑m.factorial * (b₁ * rm) →
|Real.exp 1 - Real.expNear n 1 a₁| ≤ |1| ^ n / ↑n.factorial * b₁- Defined in
- Mathlib.Analysis.Complex.Exponential
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 144 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_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- absstatement and proof · cited by 1,814
- sub_selfproof · cited by 996
- Real.expstatement and proof · cited by 871
- div_oneproof · cited by 629
- one_divproof · cited by 624
- Nat.factorialstatement and proof · cited by 616
- zero_lt_oneproof · cited by 598
Cited by2
Results whose statement or proof uses this declaration.
- Real.exp_one_near_10proof · cited by 4
- Real.exp_one_near_20proof · cited by 0