Theorems · Theorem · order theory
Nat.floor_eq_on_Ico
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] [IsStrictOrderedRing R]
(n : ℕ), ∀ a ∈ Set.Ico (↑n) (↑n + 1), ⌊a⌋₊ = 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.
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
- LinearOrderstatement and proof · cited by 8,572
- LE.le.transproof · cited by 3,151
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Set.Icostatement and proof · cited by 799
- Nat.floorstatement and proof · cited by 215
- FloorSemiringstatement and proof · cited by 179
- Nat.cast_nonnegproof · cited by 109
- Nat.floor_eq_iffproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Nat.floor_eq_on_Ico'proof · cited by 0