Theorems · Theorem · order theory
Nat.ceil_pos
∀ {α : Type u_2} [inst : Semiring α] [inst_1 : LinearOrder α] [inst_2 : FloorSemiring α] {a : α}, 0 < ⌈a⌉₊ ↔ 0 < a- Defined in
- Mathlib.Algebra.Order.Floor.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 25 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.cast_zeroproof · cited by 1,870
- FloorSemiringstatement and proof · cited by 179
- Nat.ceilstatement · cited by 141
- Nat.lt_ceilproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- Behrend.nValue_posproof · cited by 3
- Mathlib.Meta.Positivity.nat_ceil_posproof · cited by 3
- tendsto_tsum_div_pow_atTop_integralproof · cited by 1
- BoxIntegral.le_hasIntegralVertices_of_isBoundedproof · cited by 1