Theorems · Definition · field theory
DivisionRing.qsmul
{K : Type u_2} → [self : DivisionRing K] → ℚ → K → KScalar multiplication by a rational number.
Unless there is a risk of a Module ℚ _ instance diamond, write qsmul := _. This will set
qsmul to (Rat.cast · * ·) thanks to unification in the default proof of qsmul_def.
Do not use directly. Instead use the • notation.
- Defined in
- Mathlib.Algebra.Field.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- DivisionRing
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.
- DivisionRingstatement and proof · cited by 1,062
Cited by6
Results whose statement or proof uses this declaration.
- DivisionRing.qsmul_defstatement · cited by 1
- fieldOfFiniteDimensionalproof · cited by 1
- CategoryTheory.fieldEndOfFiniteDimensionalproof · cited by 0
- Field.ofIsUnitOrEqZeroproof · cited by 0
- Function.Injective.fieldproof · cited by 0
- Fintype.fieldOfDomainproof · cited by 0