embeddingDownNat — Mathlib

English

The embedding from down ℕ to up ℤ sends n to -n.

Русский

Вложение from down ℕ в up ℤ отправляет n в -n.

LaTeX

$$$\\text{embeddingDownNat}: (down\\,\\mathbb{N}) \\to (up\\,\\mathbb{Z})$ with $\\text{f}(n) = -n$$$

Lean4

/-- The embedding from `down ℕ` to `up ℤ` with sends `n` to `-n`. -/
@[simps!]
def embeddingDownNat : Embedding (down ℕ) (up ℤ) :=
  Embedding.mk' _ _ (fun n => -n) (fun _ _ h => by simpa using h) (by dsimp; cutsat)

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