lean_workbook_plus_81302

⚠️ 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.

If we call $x$ , $y$ , and $z$ the starting totals of Betty, Clare, and Al respectively. Then we have $2x+2y+(z-100)=1500\Rightarrow 2x+2y+z=1600$ . We also know that their combined net gain is $600$ . In math, $x+y-100=500\Rightarrow x+y=600$ . This is because both Betty and Clare double their initial totals and Al lost $100$ so I summed their three net outcomes. Since we know $x+y=600$ , we can plug this into the initial equation and we get $2(600)+z=1600\Rightarrow z=400$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_81302  (x y z : ℝ)
  (h₀ : 2 * x + 2 * y + (z - 100) = 1500)
  (h₁ : x + y - 100 = 500) :
  x + y + z = 1600   :=  by sorry

Conclude z=400 as requested by the source calculation, and x+y+z=1000 if reporting the total.

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

Proposed corrected statement

Conclude z=400 as requested by the source calculation, and x+y+z=1000 if reporting the total.

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.