Theorems · Theorem · ring theory
Quaternion.normSq_add
∀ {R : Type u_3} [inst : CommRing R] (a b : Quaternion R),
Quaternion.normSq (a + b) = Quaternion.normSq a + Quaternion.normSq b + 2 * (a * star b).re- Defined in
- Mathlib.Algebra.Quaternion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- CommRingstatement and proof · cited by 17,173
- Star.starstatement and proof · cited by 1,082
- MonoidWithZeroHomstatement · cited by 704
- mul_addproof · cited by 413
- add_mulproof · cited by 363
- Quaternionstatement and proof · cited by 206
- QuaternionAlgebra.restatement and proof · cited by 117
- Quaternion.normSqstatement and proof · cited by 31
- StarAddMonoid.star_addproof · cited by 29
- Quaternion.re_coeproof · cited by 4
- Quaternion.self_add_star'proof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Quaternion.normSq_expproof · cited by 1