Theorems · Theorem · order theory
Nat.preimage_ceil_of_ne_zero
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] {n : ℕ},
n ≠ 0 → Nat.ceil ⁻¹' {n} = Set.Ioc ↑(n - 1) ↑n- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- Set.preimagestatement · cited by 4,946
- Set.extproof · cited by 2,266
- Set.Iocstatement · cited by 971
- FloorSemiringstatement and proof · cited by 179
- Nat.ceilstatement · cited by 141
- Nat.ceil_eq_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Nat.measurable_ceilproof · cited by 1