Theorems · Theorem · complex analysis
Real.exp_le_exp
∀ {x y : ℝ}, Real.exp x ≤ Real.exp y ↔ x ≤ y- Defined in
- Mathlib.Analysis.Complex.Exponential
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Real.expstatement · cited by 871
- StrictMono.le_iff_leproof · cited by 104
- Real.exp_strictMonoproof · cited by 17
Cited by16
Results whose statement or proof uses this declaration.
- Real.rpow_le_rpow_of_exponent_leproof · cited by 32
- Real.log_le_log_iffproof · cited by 12
- Real.rpow_le_rpow_of_exponent_geproof · cited by 8
- ProbabilityTheory.integrable_exp_mul_of_le_of_leproof · cited by 7
- Real.exp_le_one_iffproof · cited by 6
- Real.log_le_iff_le_expproof · cited by 5
- Real.le_log_iff_exp_leproof · cited by 5
- summable_finsetProd_of_summable_nonnegproof · cited by 3
- Complex.continuousAt_cpow_zero_of_re_posproof · cited by 2
- HurwitzKernelBounds.isBigO_atTop_F_nat_oneproof · cited by 2
- ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zeroproof · cited by 1