Theorems · Theorem · ring theory
Quaternion.ext
∀ {R : Type u_3} [inst : CommRing R] (a b : Quaternion R),
a.re = b.re → a.imI = b.imI → a.imJ = b.imJ → a.imK = b.imK → a = b- Defined in
- Mathlib.Algebra.Quaternion
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Quaternionstatement and proof · cited by 206
- QuaternionAlgebra.restatement · cited by 117
- QuaternionAlgebra.imIstatement · cited by 91
- QuaternionAlgebra.imJstatement · cited by 80
- QuaternionAlgebra.imKstatement · cited by 78
- QuaternionAlgebra.extproof · cited by 21
Cited by6
Results whose statement or proof uses this declaration.
- Quaternion.normSq_eq_zeroproof · cited by 2
- Quaternion.star_improof · cited by 1
- Quaternion.coeComplex_mulproof · cited by 0
- Quaternion.ext_iffproof · cited by 0
- Quaternion.coe_real_complex_mulproof · cited by 0
- Quaternion.coeComplex_addproof · cited by 0