Theorems · Theorem · field theory
NNRat.cast_div_of_ne_zero
∀ {α : Type u_3} [inst : DivisionSemiring α] {q r : ℚ≥0}, ↑q.den ≠ 0 → ↑r.num ≠ 0 → ↑(q / r) = ↑q / ↑r- Defined in
- Mathlib.Data.Rat.Cast.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionSemiring
Around this declaration
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- div_eq_mul_invproof · cited by 715
- NNRatstatement and proof · cited by 523
- Nat.cast_mulproof · cited by 309
- NNRat.caststatement and proof · cited by 235
- DivisionSemiringstatement and proof · cited by 216
- mul_ne_zeroproof · cited by 178
- inv_divproof · cited by 92
- NNRat.numstatement and proof · cited by 53
- NNRat.denstatement and proof · cited by 51
- NNRat.cast_defproof · cited by 17
- Nat.commute_castproof · cited by 13
- Commute.div_mul_div_commproof · cited by 5
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