A sharp square-sum bound under a mixed constraint

Proved

WorkbookSource.plus_5958

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

lean-workbooksource-checked

Given $a + b^2 + c^2 = 4$ , prove that

a^2 + b^2 + c^2 \ge \frac{15}{4}

Source: InternLM Lean-Workbook, record lean_workbook_plus_5958 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_5958 (a b c : ℝ) (h : a + b^2 + c^2 = 4) : a^2 + b^2 + c^2 ≥ 15 / 4   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_5958; Apache-2.0

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