Theorems · Theorem · ring theory
QuaternionAlgebra.coe_mul
∀ {R : Type u_3} {c₁ c₂ c₃ : R} (x y : R) [inst : CommRing R], ↑(x * y) = ↑x * ↑y- Defined in
- Mathlib.Algebra.Quaternion
- Cited by
- 8 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.
Cites9
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
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- sub_selfproof · cited by 996
- sub_zeroproof · cited by 938
- QuaternionAlgebrastatement · cited by 174
- QuaternionAlgebra.coestatement · cited by 46
- QuaternionAlgebra.extproof · cited by 21
Cited by8
Results whose statement or proof uses this declaration.
- Quaternion.coe_mulproof · cited by 5
- QuaternionAlgebra.self_add_star'proof · cited by 3
- QuaternionAlgebra.star_mul_eq_coeproof · cited by 2
- QuaternionAlgebra.self_add_starproof · cited by 2
- QuaternionAlgebra.smul_coeproof · cited by 1
- Quaternion.self_add_star'proof · cited by 1
- Quaternion.star_add_self'proof · cited by 0
- Quaternion.star_eq_two_re_subproof · cited by 0