Prove2Me

Expanding a product lower bound

Proved
WorkbookSource.problem_39000

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

For real numbers y,zy,z with (y−1)(z−1)≥0(y-1)(z-1)\ge0,

yz≥y+z−1.yz\ge y+z-1.

Source: InternLM Lean-Workbook, record lean_workbook_39000 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_39000  (y z : ℝ)
  (h₀ : (y - 1) * (z - 1) ≥ 0) :
  y * z ≥ y + z - 1  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_39000; Apache-2.0

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