Theorems · Theorem · field theory
DivisionRing.ratCast_def
∀ {K : Type u_2} [self : DivisionRing K] (q : ℚ), ↑q = ↑q.num / ↑q.denHowever Rat.cast q is defined, it must be propositionally equal to q.num / q.den.
Do not use this lemma directly. Use Rat.cast_def instead.
- Defined in
- Mathlib.Algebra.Field.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- DivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Semiring.toNatCaststatement · cited by 12
- Ring.toIntCaststatement · cited by 5
- DivisionRing.toDivstatement · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Rat.cast_defproof · cited by 20
- fieldOfFiniteDimensionalproof · cited by 1
- Field.ofIsUnitOrEqZeroproof · cited by 0
- Function.Injective.fieldproof · cited by 0
- Fintype.fieldOfDomainproof · cited by 0