Theorems · Theorem · field theory
Rat.cast_mul
∀ {α : Type u_3} [inst : DivisionRing α] [CharZero α] (p q : ℚ), ↑(p * q) = ↑p * ↑q- Defined in
- Mathlib.Data.Rat.Cast.CharZero
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRingCharZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.ne'proof · cited by 1,417
- DivisionRingstatement and proof · cited by 1,062
- CharZerostatement and proof · cited by 932
- Nat.cast_ne_zeroproof · cited by 113
- Rat.posproof · cited by 17
- Rat.cast_mul_of_ne_zeroproof · cited by 1
Cited by20
Results whose statement or proof uses this declaration.
- Rat.castHomproof · cited by 33
- irrational_sqrt_ratCast_iff_of_nonnegproof · cited by 3
- isCusp_SL2Z_iffproof · cited by 3
- Irrational.mul_casesproof · cited by 3
- Irrational.mul_ratCastproof · cited by 3
- nivenproof · cited by 2
- Padic.padicNormE.mulproof · cited by 2
- Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul_sub_sqproof · cited by 1
- GaussianInt.toComplex_re_divproof · cited by 1
- niven_fract_angle_div_pi_eqproof · cited by 1
- Finpartition.IsEquipartition.card_interedges_sparsePairs_le'proof · cited by 1