nsmul — Mathlib

English

There is a scalar action of ℕ on the nonnegative subtype, sending n • ⟨x, hx⟩ to ⟨n • x, nsmul_nonneg hx n⟩.

Русский

Существуют скаляры ℕ, действующие на подпредмет: n • ⟨x, hx⟩ = ⟨n • x, nsmul_nonneg hx n⟩.

LaTeX

$$$nsmul : ℕ \\to SMul ℕ (Subtype (fun x => 0 ≤ x))$ with $nsmul$ preserving nonnegativity$$

Lean4

instance nsmul [AddMonoid α] [Preorder α] [AddLeftMono α] : SMul ℕ { x : α // 0 ≤ x } :=
  ⟨fun n x => ⟨n • (x : α), nsmul_nonneg x.prop n⟩⟩

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