Theorems · Theorem · number theory
Behrend.exp_neg_two_mul_le
∀ {x : ℝ}, 0 < x → Real.exp (-2 * x) < Real.exp (2 - ↑⌈x⌉₊) / ↑⌈x⌉₊- Cited by
- 1 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
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
- LT.lt.leproof · cited by 2,189
- Nat.cast_zeroproof · cited by 1,870
- add_commproof · cited by 1,535
- le_of_ltproof · cited by 1,175
- le_transproof · cited by 985
- Real.expstatement and proof · cited by 871
- neg_mulproof · cited by 654
- zero_lt_oneproof · cited by 598
- le_of_not_gtproof · cited by 430
- zero_le_oneproof · cited by 316
Cited by1
Results whose statement or proof uses this declaration.
- Behrend.roth_lower_bound_explicitproof · cited by 1