Theorems · Theorem · field theory
DivisionSemiring.nnratCast_def
∀ {K : Type u_2} [self : DivisionSemiring K] (q : ℚ≥0), ↑q = ↑q.num / ↑q.denHowever NNRat.cast is defined, it must be propositionally equal to a / b.
Do not use this lemma directly. Use NNRat.cast_def instead.
- Defined in
- Mathlib.Algebra.Field.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Quot.sound
- Assumes
- DivisionSemiring
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.
- NNRatstatement · cited by 523
- NNRat.caststatement · cited by 235
- DivisionSemiringstatement and proof · cited by 216
- NNRat.numstatement · cited by 53
- NNRat.denstatement · cited by 51
- Semiring.toNatCaststatement · cited by 12
- DivisionSemiring.toDivstatement · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- NNRat.cast_defproof · cited by 17
- Function.Injective.semifieldproof · cited by 0
- Function.Injective.divisionRingproof · cited by 0