Theorems · Theorem · field theory
NNRat.cast_divNat_of_ne_zero
∀ {α : Type u_3} [inst : DivisionSemiring α] (a : ℕ) {b : ℕ}, ↑b ≠ 0 → ↑(NNRat.divNat a b) = ↑a / ↑b- Defined in
- Mathlib.Data.Rat.Cast.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 71 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.cast_zeroproof · cited by 1,870
- MulZeroClass.zero_mulproof · cited by 1,625
- Nat.cast_mulproof · cited by 309
- NNRat.caststatement and proof · cited by 235
- DivisionSemiringstatement and proof · cited by 216
- NNRat.divNatstatement and proof · cited by 17
- NNRat.cast_defproof · cited by 17
- Nat.commute_castproof · cited by 13
- Rat.den_dvdproof · cited by 3
- Commute.div_eq_div_iffproof · cited by 2
- NNRat.divNat_injproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- NNRat.cast_inv_of_ne_zeroproof · cited by 1
- NNRat.cast_add_of_ne_zeroproof · cited by 1
- NNRat.cast_mul_of_ne_zeroproof · cited by 1
- NNRat.cast_div_of_ne_zeroproof · cited by 0