Theorems · Theorem · ring theory
QuaternionAlgebra.Basis.i_mul_k
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] {c₁ c₂ c₃ : R}
(q : QuaternionAlgebra.Basis A c₁ c₂ c₃), q.i * q.k = c₁ • q.j + c₂ • q.k- Defined in
- Mathlib.Algebra.QuaternionBasis
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses no axioms
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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- one_mulproof · cited by 2,841
- mul_assocproof · cited by 1,667
- add_mulproof · cited by 363
- smul_mul_assocproof · cited by 77
- QuaternionAlgebra.Basisstatement and proof · cited by 28
- QuaternionAlgebra.Basis.istatement and proof · cited by 23
- QuaternionAlgebra.Basis.jstatement and proof · cited by 23
- QuaternionAlgebra.Basis.kstatement · cited by 16
- QuaternionAlgebra.Basis.i_mul_jproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- QuaternionAlgebra.Basis.k_mul_iproof · cited by 1
- QuaternionAlgebra.Basis.lift_mulproof · cited by 0