Strict increase of a sum of two exponential functions

Proved

WorkbookRestored.plus_13994

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

The function $f(t)=4^t+9^t$ is strictly increasing on $\mathbb R$ .

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_13994 (Apache-2.0).

Preamble

import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Analysis.SpecialFunctions.Log.Basic
open Real

Formal statement

theorem WorkbookRestored.plus_13994 (f : ℝ → ℝ) (h : f = fun t ↦ 4^t + 9^t) : ∀ t₁ t₂, t₁ < t₂ → f t₁ < f t₂   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_13994; original Prove2Me node 00a504a1-8706-47b3-b5ec-1bb39e0967c0; Apache-2.0

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