Theorems · Theorem · field theory
Complex.ofReal_ne_zero
∀ {z : ℝ}, ↑z ≠ 0 ↔ z ≠ 0- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 89 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
- Complexstatement · cited by 5,565
- Complex.ofRealstatement · cited by 1,654
- Complex.ofReal_eq_zeroproof · cited by 6
Cited by46
Results whose statement or proof uses this declaration.
- Complex.norm_cpow_eq_rpow_re_of_posproof · cited by 21
- Complex.exp_logproof · cited by 14
- Real.Gamma_add_oneproof · cited by 13
- Complex.mul_cpow_ofReal_nonnegproof · cited by 12
- Complex.differentiable_Gammaℝ_invproof · cited by 6
- Complex.Gamma_ne_zeroproof · cited by 6
- Complex.ofReal_cpow_of_nonposproof · cited by 4
- sin_pi_mul_ne_zeroproof · cited by 3
- Function.Periodic.qParam_right_invproof · cited by 3
- Complex.Gamma_mul_Gamma_one_subproof · cited by 3
- Real.rpow_add_intCastproof · cited by 3
- WeakFEPair.hf_zeroproof · cited by 2