natAbs_inj_of_nonneg_of_nonpos — Mathlib

English

If a is nonnegative and b is nonpositive and their absolute values are equal, then a equals −b.

Русский

Если a ≥ 0 и b ≤ 0 и |a| = |b|, то a = −b.

LaTeX

$$$\forall a,b \in \mathbb{Z},\ a \ge 0,\ b \le 0 \Rightarrow (|a| = |b|) \iff a = -b$$$

Lean4

theorem natAbs_inj_of_nonneg_of_nonpos {a b : ℤ} (ha : 0 ≤ a) (hb : b ≤ 0) : natAbs a = natAbs b ↔ a = -b := by
  simpa only [Int.natAbs_neg] using natAbs_inj_of_nonneg_of_nonneg ha (neg_nonneg_of_nonpos hb)

Похожие утверждения