Theorems · Theorem · number theory
round_le
∀ {α : Type u_2} [inst : Ring α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [inst_3 : FloorRing α] (x : α)
(z : ℤ), |x - ↑(round x)| ≤ |x - ↑z|- Defined in
- Mathlib.Algebra.Order.Round
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- Nat.cast_oneproof · cited by 2,501
- IsStrictOrderedRingstatement and proof · cited by 2,490
- LT.lt.leproof · cited by 2,189
- absstatement and proof · cited by 1,814
- add_commproof · cited by 1,535
- FloorRingstatement and proof · cited by 405
- Int.cast_oneproof · cited by 371
- sub_add_cancelproof · cited by 344
- neg_subproof · cited by 272
- le_or_gtproof · cited by 269
Cited by3
Results whose statement or proof uses this declaration.
- AddCircle.norm_eqproof · cited by 6
- AddCircle.coe_real_preimage_closedBall_eq_iUnionproof · cited by 1
- Real.exists_nat_abs_mul_sub_round_leproof · cited by 0