Theorems · Theorem · order theory
Nat.cast_mem_Ioo_iff
∀ {α : Type u_1} [inst : Semiring α] [inst_1 : LinearOrder α] [inst_2 : FloorSemiring α] {a b : α} {n : ℕ},
0 ≤ a → (↑n ∈ Set.Ioo a b ↔ n ∈ Finset.Ioo ⌊a⌋₊ ⌈b⌉₊)- Defined in
- Mathlib.Order.Interval.Finset.Floor
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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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.Ioostatement · cited by 1,214
- Nat.floorstatement · cited by 215
- Finset.Ioostatement · cited by 185
- FloorSemiringstatement and proof · cited by 179
- Nat.ceilstatement · cited by 141
- Nat.floor_ltproof · cited by 10
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