nonneg — Mathlib

English

In ArchimedeanClass over an ordered ring, if x ≠ ⊤ and x+y = x+z then y=z.

Русский

В ArchimedeanClass над упорядоченным кольцом, если x ≠ ⊤ и x+y = x+z, то y=z.

LaTeX

$$$\forall x,y,z \in \operatorname{ArchimedeanClass}(R),\ x \neq \top \rightarrow x+y = x+z \rightarrow y=z.$$$

Lean4

theorem nonneg [Semiring R] [LinearOrder R] [ExistsAddOfLE R] [PosMulMono R] [AddLeftMono R] {x : R} (h : IsSquare x) :
    0 ≤ x := by
  rcases h with ⟨y, rfl⟩
  exact mul_self_nonneg y

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