Theorems · Theorem · complex analysis
Real.exp_neg
∀ (x : ℝ), Real.exp (-x) = (Real.exp x)⁻¹
- Defined in
- Mathlib.Analysis.Complex.Exponential
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Complex.ofRealproof · cited by 1,654
- Real.expstatement and proof · cited by 871
- Complex.expproof · cited by 612
- Complex.ofReal_negproof · cited by 130
- Complex.ofReal_invproof · cited by 62
- Complex.ofReal_expproof · cited by 44
- Complex.ofReal_injectiveproof · cited by 23
- Complex.exp_negproof · cited by 15
Cited by28
Results whose statement or proof uses this declaration.
- Real.exp_posproof · cited by 169
- Real.rpow_negproof · cited by 36
- Real.log_invproof · cited by 35
- Real.exp_subproof · cited by 13
- tendsto_rpow_mul_exp_neg_mul_atTop_nhds_zeroproof · cited by 4
- isLittleO_exp_neg_mul_rpow_atTopproof · cited by 4
- Real.add_one_lt_expproof · cited by 4
- Real.cosh_arcoshproof · cited by 3
- ProbabilityTheory.measure_ge_le_exp_mul_mgfproof · cited by 3
- Real.Gamma_integrand_isLittleOproof · cited by 2
- Real.sinh_arcoshproof · cited by 2
- Real.tendsto_exp_neg_atTop_nhds_zeroproof · cited by 2