Theorems · Theorem · order theory
Int.preimage_ceil_singleton
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] (m : ℤ),
Int.ceil ⁻¹' {m} = Set.Ioc (↑m - 1) ↑m- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Quot.sound
- Assumes
- RingLinearOrderFloorRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- Set.preimagestatement · cited by 4,946
- Set.extproof · cited by 2,266
- Set.Iocstatement · cited by 971
- FloorRingstatement and proof · cited by 405
- Int.ceilstatement · cited by 138
- Int.ceil_eq_iffproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Int.measurable_ceilproof · cited by 1