lean_workbook_plus_74833

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Given $f(g(x))=x^2$ and $g(f(x))=x^3$ , show that $f(x^3)=f(x)^2$ and $g(x^2)=g(x)^3$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_74833 (f g : ℝ → ℝ) (hf : ∀ x, f (g x) = x^2) (hg : ∀ x, g (f x) = x^3) : ∀ x, f (x^3) = f x ^ 2 ∧ g (x^2) = g x ^ 3   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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