Theorems · Definition · order theory
FloorSemiring.ceil
{α : Type u_4} → {inst : Semiring α} → {inst_1 : PartialOrder α} → [self : FloorSemiring α] → α → ℕFloorSemiring.ceil a computes the least natural n such that a ≤ (n : α).
- Defined in
- Mathlib.Algebra.Order.Floor.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- FloorSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- FloorSemiringstatement and proof · cited by 179
Cited by3
Results whose statement or proof uses this declaration.
- Nat.ceilproof · cited by 141
- FloorSemiring.gc_ceilstatement · cited by 3
- subsingleton_floorSemiringproof · cited by 0