A squared linear-form minimum on a hyperbola

Proved

WorkbookCorrected.base_16209

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

corrected-formalizationlean-workbooksource-checked

Find the minimum value of $(3x+y)^2$ given that $x^2 - y^2 = 1$ .

Source: InternLM Lean-Workbook, record lean_workbook_16209 (Apache-2.0). Natural-language proposition preserved; the source bound is completed with an exact attainment witness. Proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookCorrected.base_16209 : (∀ (x y : ℝ) (h : x^2 - y^2 = 1), 8 ≤ (3*x + y)^2) ∧ (∃ x y : ℝ, (x^2 - y^2 = 1) ∧ ( 8  =  (3*x + y)^2  )) := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_16209; Apache-2.0

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