Theorems · Theorem · order theory
Nat.cast_mem_Ioc_iff
∀ {α : Type u_1} [inst : Semiring α] [inst_1 : LinearOrder α] [inst_2 : FloorSemiring α] {a b : α} {n : ℕ},
0 ≤ a → 0 ≤ b → (↑n ∈ Set.Ioc a b ↔ n ∈ Finset.Ioc ⌊a⌋₊ ⌊b⌋₊)- Defined in
- Mathlib.Order.Interval.Finset.Floor
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Finsetstatement · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- Set.Iocstatement · cited by 971
- Finset.Iocstatement · cited by 301
- Nat.floorstatement · cited by 215
- FloorSemiringstatement and proof · cited by 179
- Nat.le_floor_iffproof · cited by 24
- Nat.floor_ltproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Nat.cast_mem_Ioc_iff'proof · cited by 0