The square function is not injective

Proved

WorkbookSource.plus_21270

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

lean-workbooksource-checked

Function $f(x)=x^2$ is not one-one

Source: InternLM Lean-Workbook, record lean_workbook_plus_21270 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_21270 (f : ℝ → ℝ) (h₁ : ∀ x, f x = x^2) : ¬ (∀ x y, f x = f y → x = y)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_21270; Apache-2.0

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