Theorems · Theorem · ring theory
Quaternion.sq_eq_neg_normSq
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : Quaternion R},
a ^ 2 = -↑(Quaternion.normSq a) ↔ a.re = 0- Defined in
- Mathlib.Algebra.Quaternion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- LinearOrderstatement and proof · cited by 8,572
- IsStrictOrderedRingstatement and proof · cited by 2,490
- map_zeroproof · cited by 1,614
- eq_or_neproof · cited by 1,117
- Star.starproof · cited by 1,082
- MonoidWithZeroHomstatement · cited by 704
- mul_negproof · cited by 590
- neg_zeroproof · cited by 542
- zero_powproof · cited by 361
- sqproof · cited by 280
Cited by2
Results whose statement or proof uses this declaration.
- Quaternion.expSeries_even_of_imaginaryproof · cited by 1
- Quaternion.expSeries_odd_of_imaginaryproof · cited by 1