Theorems · Theorem · number theory
Rat.fract_inv_num_lt_num_of_pos
∀ {q : ℚ}, 0 < q → (Int.fract q⁻¹).num < q.num- Defined in
- Mathlib.Data.Rat.Floor
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- mul_commproof · cited by 2,262
- LT.lt.leproof · cited by 2,189
- ne_of_gtproof · cited by 637
- div_oneproof · cited by 629
- Int.cast_natCastproof · cited by 393
- abs_of_nonnegproof · cited by 279
- Int.floorproof · cited by 225
- Int.fractstatement and proof · cited by 114
- Nat.cast_natAbsproof · cited by 30
- sub_lt_iff_lt_add'proof · cited by 30
Cited by1
Results whose statement or proof uses this declaration.
- GenContFract.IntFractPair.of_inv_fr_num_lt_num_of_posproof · cited by 1