Theorems · Theorem · number theory
abs_sub_round_eq_min
∀ {α : Type u_2} [inst : Ring α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [inst_3 : FloorRing α] (x : α),
|x - ↑(round x)| = min (Int.fract x) (1 - Int.fract x)- Defined in
- Mathlib.Algebra.Order.Round
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- IsStrictOrderedRingstatement and proof · cited by 2,490
- absstatement and proof · cited by 1,814
- LT.lt.neproof · cited by 872
- zero_lt_oneproof · cited by 598
- lt_of_lt_of_leproof · cited by 438
- FloorRingstatement and proof · cited by 405
- not_ltproof · cited by 306
- two_mulproof · cited by 232
- Int.floorproof · cited by 225
- lt_or_geproof · cited by 182
Cited by3
Results whose statement or proof uses this declaration.
- AddCircle.norm_eqproof · cited by 6
- round_leproof · cited by 3
- abs_sub_round_div_natCast_eqproof · cited by 1