lean_workbook_plus_67402

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Then $3 \cdot \frac{2t}{1+t^{2}}+ \sqrt{3} \cdot \frac{1-t^{2}}{1+t^{2}} + \sqrt{3} =4 \cdot \frac{2t}{1+t^{2}} \cdot \frac{1-t^{2}}{1+t^{2}}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_67402 : ∀ t : ℝ, 3 * (2 * t / (1 + t ^ 2)) + Real.sqrt 3 * ((1 - t ^ 2) / (1 + t ^ 2)) + Real.sqrt 3 = 4 * (2 * t / (1 + t ^ 2)) * ((1 - t ^ 2) / (1 + t ^ 2))   :=  by sorry

The source begins “Then” and supplies no prior premise, so the intended domain cannot be reconstructed.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Restore the prior equation that t must satisfy, or treat the displayed equality as an equation to solve rather than an identity for every real t.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.