Theorems · Theorem · number theory
Rat.num_den_mk
∀ {q : ℚ} {n d : ℤ}, d ≠ 0 → q = Rat.divInt n d → ∃ c, n = c * q.num ∧ d = c * ↑q.den- Defined in
- Mathlib.Data.Rat.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- eq_or_neproof · cited by 1,117
- Rat.num_ne_zeroproof · cited by 5
- Rat.divInt_ne_zeroproof · cited by 3
- Int.eq_mul_div_of_mul_eq_mul_of_dvd_leftproof · cited by 1
- Rat.num_dvdproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Rat.exists_eq_mul_div_num_and_eq_mul_div_denproof · cited by 3
- padicValRat.defnproof · cited by 2