Theorems · Theorem · order theory
Complex.not_le_zero_iff
∀ {z : ℂ}, ¬z ≤ 0 ↔ 0 < z.re ∨ z.im ≠ 0- Defined in
- Mathlib.Analysis.Complex.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Complex.restatement · cited by 882
- Complex.imstatement · cited by 591
- Complex.partialOrderstatement · cited by 64
- Complex.not_le_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Complex.mem_slitPlane_iff_not_le_zeroproof · cited by 1
- Complex.continuousAt_cpow_of_re_posproof · cited by 1