Theorems · Theorem · field theory
Complex.normSq_sub
∀ (z w : ℂ), Complex.normSq (z - w) = Complex.normSq z + Complex.normSq w - 2 * (z * (starRingEnd ℂ) w).re
- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 107 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.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHomstatement · cited by 10,189
- Complexstatement and proof · cited by 5,565
- sub_eq_add_negproof · cited by 1,023
- Complex.restatement and proof · cited by 882
- MonoidWithZeroHomstatement · cited by 704
- starRingEndstatement and proof · cited by 671
- mul_negproof · cited by 590
- map_negproof · cited by 378
- Complex.normSqstatement and proof · cited by 103
- Complex.normSq_negproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- UpperHalfPlane.cosh_half_distproof · cited by 3
- LinearIsometry.im_apply_eq_improof · cited by 1