Theorems · Theorem · order theory
Int.abs_sub_lt_one_of_floor_eq_floor
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] [IsOrderedRing R] {a b : R},
⌊a⌋ = ⌊b⌋ → |a - b| < 1- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- absstatement · cited by 1,814
- IsOrderedRingstatement and proof · cited by 777
- FloorRingstatement and proof · cited by 405
- abs_of_nonnegproof · cited by 279
- Int.floorstatement and proof · cited by 225
- add_sub_cancel_leftproof · cited by 198
- le_of_not_geproof · cited by 72
- sub_le_sub_leftproof · cited by 43
- abs_sub_commproof · cited by 40
- sub_nonneg_of_leproof · cited by 37
Cited by3
Results whose statement or proof uses this declaration.
- Real.exists_int_int_abs_mul_sub_leproof · cited by 2
- AbsoluteValue.exists_partition_intproof · cited by 0
- GromovHausdorff.totallyBoundedproof · cited by 0