Theorems · Definition · ring theory
QuaternionAlgebra.imI
{R : Type u_1} → {a b c : R} → QuaternionAlgebra R a b c → RFirst imaginary part (i) of a quaternion.
- Defined in
- Mathlib.Algebra.Quaternion
- Cited by
- 91 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- QuaternionAlgebrastatement and proof · cited by 174
Cited by99
Results whose statement or proof uses this declaration.
- QuaternionAlgebra.extstatement and proof · cited by 21
- QuaternionAlgebra.improof · cited by 20
- Quaternion.dualNumberEquivproof · cited by 16
- QuaternionAlgebra.equivProdproof · cited by 8
- QuaternionAlgebra.swapEquivproof · cited by 8
- QuaternionAlgebra.Basis.liftproof · cited by 6
- QuaternionAlgebra.equivTupleproof · cited by 6
- Quaternion.extstatement · cited by 6
- Quaternion.linearIsometryEquivTupleproof · cited by 6
- Quaternion.normSq_def'statement and proof · cited by 5
- Quaternion.re_starproof · cited by 4
- Quaternion.re_mulstatement and proof · cited by 3