instFloorDiv — Mathlib

English

The natural CeilDiv is implemented via ceilDiv a b = (a + b − 1) / b with associated properties.

Русский

Nat CeilDiv реализуется через ceilDiv a b = (a + b − 1) / b с сопутствующими свойствами.

LaTeX

$$$ ceilDiv(a,b) = (a + b - 1) / b \\quad (a,b \\in \\mathbb{N}).$$$

Lean4

instance instFloorDiv : FloorDiv ℕ ℕ where
  floorDiv := HDiv.hDiv
  floorDiv_gc a ha := by simpa [mul_comm] using Nat.galoisConnection_mul_div ha
  floorDiv_nonpos a ha b := by rw [ha.antisymm <| zero_le _, Nat.div_zero]
  zero_floorDiv := Nat.zero_div

Похожие утверждения