Subadditivity of fractional real powers

Proved

WorkbookTyped.plus_72873

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

lean-workbookrepaired-variable-declarationssource-checked

Let $x,y > 0$ and $t\in (0,1)$ . Prove $(x + y)^t\le x^t + y^t.$

Source declaration repair: Added the explicit real binder t, as required by the source condition t ∈ (0,1), so all three powers use Real.rpow. The malformed declaration and its possible vacuous natural-number interpretation are not retained. A genuine real-power proof replaces the original tactic attempts.

Source: InternLM Lean-Workbook, record lean_workbook_plus_72873 (Apache-2.0). The original source declaration omits t; this public record supplies its intended real type.

Preamble

import Mathlib

Formal statement

theorem WorkbookTyped.plus_72873 (x y t : ℝ) (hx : 0 < x) (hy : 0 < y) (h : 0 < t ∧ t < 1) :
  (x + y)^t ≤ x^t + y^t   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_72873; explicit variable-declaration repair; Apache-2.0

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