lean_workbook_plus_15404

⚠️ Retired — specification defect

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

Example $f(x)=\{\begin{array}{ll}x+{1\over 3}& \text{for }\{x\}\in [0,{2\over 3})\ &\ x-{2\over 3}& \text{for }\{x\}\in [{2\over 3},1) \end{array}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_15404  (f : ℝ → ℝ)
  (h₀ : ∀ x, (x ∈ Set.Icc 0 (2 / 3)) → f x = x + 1 / 3)
  (h₁ : ∀ x, (x ∈ Set.Icc (2 / 3) 1) → f x = x - 2 / 3) :
  Continuous f  :=  by sorry

The two posted closed intervals overlap at2/3 and demand the distinct values0 and1.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Use the fractional part of x in the source’s half-open intervals[0,2/3) and[2/3,1), and define the map by those disjoint cases. Remove the invented continuity claim; this map jumps at2/3.

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.