An exponential comparison with a radical exponent

Proved

WorkbookSource.base_1159

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

lean-workbooksource-checked

So $4^{x+1}>3^{\sqrt{x^2+1}}$ for $x>0$

Source: InternLM Lean-Workbook, record lean_workbook_1159 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_1159 (x : ℝ) (hx: x > 0) : (4:ℝ)^(x + 1) > 3^(Real.sqrt (x^2 + 1))  :=  by sorry

Source