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Theorems · Definition · field theory

DivisionSemiring.nnqsmul

{K : Type u_2} → [self : DivisionSemiring K] → ℚ≥0 → K → K

Scalar multiplication by a nonnegative rational number. Unless there is a risk of a Module ℚ≥0 _ instance diamond, write nnqsmul := _. This will set nnqsmul to (NNRat.cast · * ·) thanks to unification in the default proof of nnqsmul_def. Do not use directly. Instead use the • notation.

Defined in
Mathlib.Algebra.Field.Defs
Cited by
1 results in Mathlib
Foundations
Depth 40 from the axioms · uses propext, Quot.sound
Assumes
DivisionSemiring
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

DivisionSemiring.nnqsmul_def · cited by 1DivisionSemiring.nnqsmul_…Function.Injective.semifield · cited by 0Injective.semifieldFunction.Injective.divisionRing · cited by 0Injective.divisionRingNNRat · cited by 523NNRatDivisionSemiring · cited by 216DivisionSemiringDivisionSemiring.nnqsmulCITED BYCITES

Cites2

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Cited by3

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