Theorems · Theorem · ring theory
QuaternionAlgebra.coe_add
∀ {R : Type u_3} {c₁ c₂ c₃ : R} (x y : R) [inst : AddZeroClass R], ↑(x + y) = ↑x + ↑y- Defined in
- Mathlib.Algebra.Quaternion
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
- Assumes
- AddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_zeroproof · cited by 2,707
- AddZeroClassstatement and proof · cited by 1,237
- QuaternionAlgebrastatement · cited by 174
- QuaternionAlgebra.coestatement · cited by 46
- QuaternionAlgebra.extproof · cited by 21
Cited by4
Results whose statement or proof uses this declaration.
- QuaternionAlgebra.self_add_star'proof · cited by 3
- QuaternionAlgebra.star_mul_eq_coeproof · cited by 2
- QuaternionAlgebra.self_add_starproof · cited by 2
- Quaternion.coe_addproof · cited by 0