Theorems · Theorem · order theory
Int.fract_eq_iff
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] [IsOrderedRing R] {a b : R},
Int.fract a = b ↔ 0 ≤ b ∧ b < 1 ∧ ∃ z, a - b = ↑z- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- add_zeroproof · cited by 2,707
- add_commproof · cited by 1,535
- sub_eq_add_negproof · cited by 1,023
- IsOrderedRingstatement and proof · cited by 777
- add_assocproof · cited by 746
- FloorRingstatement and proof · cited by 405
- Int.floorproof · cited by 225
- Int.fractstatement and proof · cited by 114
- sub_sub_cancelproof · cited by 105
- eq_sub_iff_add_eqproof · cited by 65
Cited by4
Results whose statement or proof uses this declaration.
- Int.fract_div_natCast_eq_div_natCast_modproof · cited by 3
- Int.fract_eq_selfproof · cited by 1
- Int.fract_eq_fractproof · cited by 0
- Int.fract_negproof · cited by 0