Nat.floor

{α : Type u_2} → [inst : Semiring α] → [inst_1 : PartialOrder α] → [FloorSemiring α] → α → ℕ

⌊a⌋₊ is the greatest natural n such that n ≤ a. If a is negative, then ⌊a⌋₊ = 0.

Defined in: Mathlib.Algebra.Order.Floor.Defs
Cited by: 215 results in Mathlib
Foundations: Depth 3 from the axioms, rests on 6 definitions · uses no axioms
Assumes: Semiring PartialOrder FloorSemiring

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 227.