Theorems · Theorem · order theory
Nat.le_floor_iff
∀ {α : Type u_2} [inst : Semiring α] [inst_1 : PartialOrder α] [inst_2 : FloorSemiring α] {a : α} {n : ℕ},
0 ≤ a → (n ≤ ⌊a⌋₊ ↔ ↑n ≤ a)- Defined in
- Mathlib.Algebra.Order.Floor.Defs
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- Nat.floorstatement · cited by 215
- FloorSemiringstatement and proof · cited by 179
- FloorSemiring.gc_floorproof · cited by 3
Cited by24
Results whose statement or proof uses this declaration.
- Nat.floor_leproof · cited by 21
- Nat.floor_natCastproof · cited by 19
- Nat.le_floorproof · cited by 11
- Nat.floor_ltproof · cited by 10
- Nat.le_floor_iff'proof · cited by 7
- Nat.floor_eq_iffproof · cited by 5
- NumberField.hermiteTheorem.rank_le_rankOfDiscrBddproof · cited by 4
- sum_mul_eq_sub_sub_integral_mulproof · cited by 4
- Nat.floor_add_natCastproof · cited by 4
- integrableOn_mul_sum_Iccproof · cited by 3
- SimpleGraph.extremalNumber_le_iff_of_nonnegproof · cited by 2
- NumberField.Ideal.tendsto_norm_le_div_atTop₀proof · cited by 2