Theorems · Theorem · complex analysis
Complex.norm_sub_one_sq_eq_of_norm_eq_one
∀ {z : ℂ}, ‖z‖ = 1 → ‖z - 1‖ ^ 2 = 2 * (1 - z.re)- Defined in
- Mathlib.Analysis.Complex.Norm
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Norm.normstatement and proof · cited by 5,413
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- sub_zeroproof · cited by 938
- Complex.restatement and proof · cited by 882
- Complex.improof · cited by 591
- neg_eq_zeroproof · cited by 171
- sub_eq_zero_of_eqproof · cited by 154
- sq_eq_one_iffproof · cited by 14
- Complex.normSq_applyproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Unitary.two_mul_one_sub_le_norm_sub_one_sqproof · cited by 2
- Complex.norm_sub_one_sq_eqOn_sphereproof · cited by 1