Lean-Workbook Plus 33186: Exponential inequality

Proved

WorkbookRestored.plus_33186

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

lean-workbookrestored-importssource-checked

For real $c,x$ , $e^{cx}>0$ .

Source: Lean-Workbook row lean_workbook_plus_33186 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble

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

Formal statement

theorem WorkbookRestored.plus_33186 (x : ℝ) (c : ℝ) : 0 < exp (c * x)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_33186; immutable original Prove2Me node 81f2dab6-67e4-49c2-833c-4a50168df7fb

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