Theorems · Theorem · field theory
Rat.cast_div_of_ne_zero
∀ {α : Type u_3} [inst : DivisionRing α] {p q : ℚ}, ↑p.den ≠ 0 → ↑q.num ≠ 0 → ↑(p / q) = ↑p / ↑q- Defined in
- Mathlib.Data.Rat.Cast.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRing
Around this declaration
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Cites12
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
- div_eq_mul_invproof · cited by 715
- Int.cast_natCastproof · cited by 393
- mul_ne_zeroproof · cited by 178
- Int.cast_mulproof · cited by 113
- inv_divproof · cited by 92
- Rat.cast_defproof · cited by 20
- Nat.commute_castproof · cited by 13
- Commute.div_mul_div_commproof · cited by 5
- Rat.cast_divInt_of_ne_zeroproof · cited by 5
- Int.commute_castproof · cited by 5
- Rat.div_def'proof · cited by 3
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