Theorems · Theorem · field theory
DivisionRing.nnratCast_def
∀ {K : Type u_2} [self : DivisionRing K] (q : ℚ≥0), ↑q = ↑q.num / ↑q.denHowever NNRat.cast is defined, it must be equal to a / b.
Do not use this lemma directly. Use NNRat.cast_def instead.
- Defined in
- Mathlib.Algebra.Field.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Quot.sound
- Assumes
- DivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- NNRatstatement · cited by 523
- NNRat.caststatement · cited by 235
- NNRat.numstatement · cited by 53
- NNRat.denstatement · cited by 51
- Semiring.toNatCaststatement · cited by 12
- DivisionRing.toDivstatement · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- fieldOfFiniteDimensionalproof · cited by 1
- Field.ofIsUnitOrEqZeroproof · cited by 0
- Function.Injective.fieldproof · cited by 0
- Fintype.fieldOfDomainproof · cited by 0