Theorems · Theorem · complex analysis
Real.exp_pos
∀ (x : ℝ), 0 < Real.exp x
- Defined in
- Mathlib.Analysis.Complex.Exponential
- Cited by
- 169 results in Mathlib
- Foundations
- Depth 149 from the axioms, rests on 4,042 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- neg_negproof · cited by 960
- Real.expstatement and proof · cited by 871
- zero_lt_oneproof · cited by 598
- lt_of_lt_of_leproof · cited by 438
- le_totalproof · cited by 294
- inv_posproof · cited by 124
- neg_nonnegproof · cited by 60
- Real.exp_negproof · cited by 28
- Real.one_le_expproof · cited by 2
Cited by170
Results whose statement or proof uses this declaration.
- Real.rpow_pos_of_posproof · cited by 155
- Real.rpow_nonnegproof · cited by 111
- Real.log_expproof · cited by 33
- Real.log_rpowproof · cited by 31
- Real.abs_expproof · cited by 23
- Real.exp_nonnegproof · cited by 21
- Real.exp_strictMonoproof · cited by 17
- Real.Gamma_pos_of_posproof · cited by 17
- Real.exp_mulproof · cited by 13
- ProbabilityTheory.mgf_pos'proof · cited by 9
- MeasureTheory.integral_exp_posproof · cited by 8
- ProbabilityTheory.integrable_exp_mul_of_le_of_leproof · cited by 7