Theorems · Theorem · complex analysis
Real.pow_div_factorial_le_exp
∀ (x : ℝ), 0 ≤ x → ∀ (n : ℕ), x ^ n / ↑n.factorial ≤ Real.exp x
- Defined in
- Mathlib.Analysis.Complex.Exponential
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- Finset.rangeproof · cited by 1,341
- Real.expstatement · cited by 871
- Nat.factorialstatement · cited by 616
- Nat.cast_pos'proof · cited by 219
- pow_nonnegproof · cited by 141
- Nat.factorial_posproof · cited by 99
- Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_posproof · cited by 58
- Finset.single_le_sumproof · cited by 34
- Real.sum_le_exp_of_nonnegproof · cited by 5
- Finset.self_mem_range_succproof · cited by 4
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