Theorems · Definition · order theory
Int.fract
{α : Type u_2} → [inst : Ring α] → [inst_1 : LinearOrder α] → [FloorRing α] → α → αInt.fract a the fractional part of a, is a minus its floor.
- Defined in
- Mathlib.Algebra.Order.Floor.Defs
- Cited by
- 114 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 122 definitions · uses no axioms
- Assumes
- RingLinearOrderFloorRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- FloorRingstatement and proof · cited by 405
- Int.floorproof · cited by 225
Cited by117
Results whose statement or proof uses this declaration.
- roundproof · cited by 49
- GenContFract.IntFractPair.ofproof · cited by 22
- Int.fract_lt_onestatement · cited by 20
- Int.fract_nonnegstatement · cited by 17
- Int.fract_intCaststatement · cited by 8
- Int.fract_zerostatement · cited by 6
- ZSpan.repr_fract_applystatement and proof · cited by 6
- AddCircle.norm_eqproof · cited by 6
- Int.floor_add_fractstatement · cited by 4
- Int.fract_eq_iffstatement and proof · cited by 4
- round_add_intCastproof · cited by 4
- abs_sub_round_eq_minstatement and proof · cited by 3