Theorems · Theorem · ring theory
Quaternion.star_mul_self
∀ {R : Type u_3} [inst : CommRing R] (a : Quaternion R), star a * a = ↑(Quaternion.normSq a)- Defined in
- Mathlib.Algebra.Quaternion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 1,082
- MonoidWithZeroHomstatement · cited by 704
- Quaternionstatement and proof · cited by 206
- Quaternion.coestatement and proof · cited by 68
- Quaternion.normSqstatement and proof · cited by 31
- IsStarNormal.star_comm_selfproof · cited by 8
- Quaternion.self_mul_starproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Quaternion.sq_eq_neg_normSqproof · cited by 2
- Quaternion.sq_eq_normSqproof · cited by 0