Theorems · Theorem · ring theory
QuaternionAlgebra.Basis.lift_mul
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] {c₁ c₂ c₃ : R}
(q : QuaternionAlgebra.Basis A c₁ c₂ c₃) (x y : QuaternionAlgebra R c₁ c₂ c₃), q.lift (x * y) = q.lift x * q.lift y- Defined in
- Mathlib.Algebra.QuaternionBasis
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites46
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- mul_commproof · cited by 2,262
- Nat.cast_zeroproof · cited by 1,870
Cited by1
Results whose statement or proof uses this declaration.
- QuaternionAlgebra.Basis.liftHomproof · cited by 3