Theorems · Theorem · field theory
Rat.cast_divInt_of_ne_zero
∀ {α : Type u_3} [inst : DivisionRing α] (a : ℤ) {b : ℤ}, ↑b ≠ 0 → ↑(Rat.divInt a b) = ↑a / ↑b- Defined in
- Mathlib.Data.Rat.Cast.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 67 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- mul_assocproof · cited by 1,667
- MulZeroClass.zero_mulproof · cited by 1,625
- DivisionRingstatement and proof · cited by 1,062
- div_eq_mul_invproof · cited by 715
- ne_of_gtproof · cited by 637
- Int.cast_natCastproof · cited by 393
- mul_inv_cancel₀proof · cited by 210
- Int.cast_zeroproof · cited by 188
- Ne.bot_ltproof · cited by 116
- Int.cast_mulproof · cited by 113
- Commute.eqproof · cited by 91
Cited by5
Results whose statement or proof uses this declaration.
- Rat.cast_injectiveproof · cited by 5
- Rat.cast_mkRat_of_ne_zeroproof · cited by 2
- Rat.cast_inv_of_ne_zeroproof · cited by 1
- Rat.cast_div_of_ne_zeroproof · cited by 0
- AddCircle.addOrderOf_coe_ratproof · cited by 0