Theorems · Theorem · order theory
Complex.nonneg_iff
∀ {z : ℂ}, 0 ≤ z ↔ 0 ≤ z.re ∧ 0 = z.im- Defined in
- Mathlib.Analysis.Complex.Order
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 110 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.le_defproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Complex.sq_nonneg_iffproof · cited by 1
- Differentiable.nonneg_of_iteratedDeriv_nonnegproof · cited by 1
- Complex.arg_eq_zero_iff_zero_leproof · cited by 0