Theorems · Theorem · field theory
Rat.cast_mul_of_ne_zero
∀ {α : Type u_3} [inst : DivisionRing α] {p q : ℚ}, ↑p.den ≠ 0 → ↑q.den ≠ 0 → ↑(p * q) = ↑p * ↑q- Defined in
- Mathlib.Data.Rat.Cast.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Nat.cast_mulproof · cited by 309
- mul_ne_zeroproof · cited by 178
- Int.cast_mulproof · cited by 113
- Rat.cast_defproof · cited by 20
- Nat.commute_castproof · cited by 13
- Commute.div_mul_div_commproof · cited by 5
- Int.commute_castproof · cited by 5
- Rat.mul_eq_mkRatproof · cited by 3
- Rat.cast_mkRat_of_ne_zeroproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Rat.cast_mulproof · cited by 19