Theorems · Theorem · complex analysis
Real.exp_lt_one_iff
∀ {x : ℝ}, Real.exp x < 1 ↔ x < 0- Defined in
- Mathlib.Analysis.Complex.Exponential
- Cited by
- 7 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.
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 and proof · cited by 871
- Real.exp_zeroproof · cited by 81
- Real.exp_lt_expproof · cited by 11
Cited by7
Results whose statement or proof uses this declaration.
- UpperHalfPlane.norm_qParam_lt_oneproof · cited by 5
- Real.Gamma_three_div_two_lt_oneproof · cited by 2
- Real.summable_pow_mul_exp_neg_nat_mulproof · cited by 1
- UpperHalfPlane.qExpansion_coeff_eq_intervalIntegralproof · cited by 1
- Real.rpow_lt_one_iff_of_posproof · cited by 1
- norm_jacobiTheta_sub_one_leproof · cited by 1
- norm_exp_mul_sq_leproof · cited by 1