Theorems · Theorem · field theory
NNRat.cast_mul_of_ne_zero
∀ {α : Type u_3} [inst : DivisionSemiring α] {q r : ℚ≥0}, ↑q.den ≠ 0 → ↑r.den ≠ 0 → ↑(q * r) = ↑q * ↑r- Defined in
- Mathlib.Data.Rat.Cast.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- NNRat.numproof · 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
- NNRat.cast_divNat_of_ne_zeroproof · cited by 4
- NNRat.mul_defproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- NNRat.cast_mulproof · cited by 5