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Theorems · Definition · ring theory

Quaternion.equivProd

(R : Type u_1) → [inst : Zero R] → [inst_1 : One R] → [inst_2 : Neg R] → Quaternion R ≃ R × R × R × R

The equivalence between the quaternions over R and R × R × R × R.

Defined in
Mathlib.Algebra.Quaternion
Cited by
5 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
ZeroOneNeg
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Quaternion.imJ_equivProd_symm_apply · cited by 0Quaternion.imJ_equivProd_…Quaternion.imI_equivProd_symm_apply · cited by 0Quaternion.imI_equivProd_…Quaternion.imK_equivProd_symm_apply · cited by 0Quaternion.imK_equivProd_…Quaternion.equivProd_apply · cited by 0Quaternion.equivProd_applyQuaternion.re_equivProd_symm_apply · cited by 0Quaternion.re_equivProd_s…Equiv · cited by 8337EquivQuaternion · cited by 206QuaternionQuaternionAlgebra.equivProd · cited by 8QuaternionAlgebra.equivPr…Quaternion.equivProdCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.