Theorems · Theorem · ring theory
QuaternionAlgebra.coe_smul
∀ {S : Type u_1} {R : Type u_3} {c₁ c₂ c₃ : R} [inst : Zero R] [inst_1 : SMulZeroClass S R] (s : S) (r : R),
↑(s • r) = s • ↑r- Defined in
- Mathlib.Algebra.Quaternion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- ZeroSMulZeroClass
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.
- smul_zeroproof · cited by 665
- SMulZeroClassstatement and proof · cited by 213
- QuaternionAlgebrastatement · cited by 174
- QuaternionAlgebra.coestatement · cited by 46
- QuaternionAlgebra.extproof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- Quaternion.coe_smulproof · cited by 0