A quartic polynomial is positive on the open unit interval

Proved

WorkbookSource.base_5683

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

lean-workbooksource-checked

Prove $13a^4-26a^2+13a+1>0$ for $0<a<1$ .

Source: InternLM Lean-Workbook, record lean_workbook_5683 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_5683 (a : ℝ) (h1 : 0 < a) (h2 : a < 1) : 13*a^4 - 26*a^2 + 13*a + 1 > 0  :=  by sorry

Source