Theorems · Theorem · order theory
Nat.floor_lt
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] {a : R} {n : ℕ},
0 ≤ a → (⌊a⌋₊ < n ↔ a < ↑n)- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext
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.
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- Nat.floorstatement · cited by 215
- FloorSemiringstatement and proof · cited by 179
- lt_iff_lt_of_le_iff_leproof · cited by 54
- Nat.le_floor_iffproof · cited by 24
Cited by10
Results whose statement or proof uses this declaration.
- Nat.floor_eq_iffproof · cited by 5
- sum_mul_eq_sub_sub_integral_mulproof · cited by 4
- integrableOn_mul_sum_Iccproof · cited by 3
- Nat.floor_lt_ceil_of_lt_of_posproof · cited by 1
- Nat.cast_mem_Ioc_iffproof · cited by 1
- Nat.floor_lt_oneproof · cited by 0
- SimpleGraph.lt_zarankiewicz_iff_of_nonnegproof · cited by 0
- Nat.cast_mem_Ioi_iffproof · cited by 0
- Nat.cast_mem_Ioo_iffproof · cited by 0
- SimpleGraph.lt_extremalNumber_iff_of_nonnegproof · cited by 0