Theorems · Theorem · order theory
Complex.sq_nonneg_iff
∀ {z : ℂ}, 0 ≤ z ^ 2 ↔ z.im = 0- Defined in
- Mathlib.Analysis.Complex.Order
- Cited by
- 1 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.
Cites17
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 and proof · cited by 5,565
- mul_commproof · cited by 2,262
- sub_zeroproof · cited by 938
- Complex.reproof · cited by 882
- Complex.imstatement and proof · cited by 591
- zero_powproof · cited by 361
- two_ne_zeroproof · cited by 251
- pow_twoproof · cited by 150
- Complex.mul_reproof · cited by 115
- Complex.mul_improof · cited by 107
- sq_nonnegproof · cited by 106
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.sign_discrproof · cited by 1