Theorems · Definition · ring theory
QuaternionAlgebra.coe
{R : Type u_3} → {c₁ c₂ c₃ : R} → [Zero R] → R → QuaternionAlgebra R c₁ c₂ c₃Coercion R → ℍ[R,c₁,c₂,c₃].
- Defined in
- Mathlib.Algebra.Quaternion
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- Zero
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 · cited by 174
Cited by47
Results whose statement or proof uses this declaration.
- Quaternion.coeproof · cited by 68
- QuaternionAlgebra.coe_mulstatement · cited by 8
- QuaternionAlgebra.coe_addstatement · cited by 4
- QuaternionAlgebra.coe_commutesstatement · cited by 3
- QuaternionAlgebra.coe_mul_eq_smulstatement · cited by 3
- QuaternionAlgebra.self_add_star'statement and proof · cited by 3
- QuaternionAlgebra.coe_injectivestatement and proof · cited by 2
- QuaternionAlgebra.coe_negstatement · cited by 2
- QuaternionAlgebra.eq_re_of_eq_coestatement and proof · cited by 2
- QuaternionAlgebra.self_add_starstatement and proof · cited by 2
- QuaternionAlgebra.star_add_self'statement and proof · cited by 2
- QuaternionAlgebra.star_coestatement · cited by 2