Theorems · Theorem · order theory
Int.floor_nonneg
∀ {α : Type u_2} [inst : Ring α] [inst_1 : LinearOrder α] [inst_2 : FloorRing α] {a : α}, 0 ≤ ⌊a⌋ ↔ 0 ≤ a- Defined in
- Mathlib.Algebra.Order.Floor.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext
- Assumes
- RingLinearOrderFloorRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- FloorRingstatement and proof · cited by 405
- Int.floorstatement · cited by 225
- Int.cast_zeroproof · cited by 188
- Int.le_floorproof · cited by 22
Cited by5
Results whose statement or proof uses this declaration.
- Int.natCast_floor_eq_floorproof · cited by 4
- Real.exists_int_int_abs_mul_sub_leproof · cited by 2
- Mathlib.Meta.Positivity.int_floor_nonnegproof · cited by 1
- AbsoluteValue.exists_partition_intproof · cited by 0
- GromovHausdorff.totallyBoundedproof · cited by 0