Theorems · Theorem · complex analysis
Complex.exp_ne_zero
∀ (x : ℂ), Complex.exp x ≠ 0
- Defined in
- Mathlib.Analysis.Complex.Exponential
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- MulZeroClass.zero_mulproof · cited by 1,625
- Complex.expstatement and proof · cited by 612
- add_neg_cancelproof · cited by 213
- zero_ne_oneproof · cited by 90
- Complex.exp_addproof · cited by 55
- Complex.exp_zeroproof · cited by 43
Cited by19
Results whose statement or proof uses this declaration.
- Complex.exp_negproof · cited by 15
- Real.exp_ne_zeroproof · cited by 7
- Complex.cos_eq_zero_iffproof · cited by 5
- Function.Periodic.eq_cuspFunctionproof · cited by 4
- Function.Periodic.qParam_tendstoproof · cited by 3
- Complex.range_expproof · cited by 3
- Function.Periodic.differentiableAt_cuspFunctionproof · cited by 2
- UpperHalfPlane.isBoundedAtImInfty_of_hasSum_qExpansionproof · cited by 1
- Complex.angle_exp_expproof · cited by 1
- Complex.exp_eq_exp_iff_exp_sub_eq_oneproof · cited by 1
- Complex.isAddQuotientCoveringMap_expstatement and proof · cited by 1
- UpperHalfPlane.qExpansion_coeff_eq_intervalIntegralproof · cited by 1