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    $\begingroup$ Not a very elegant solution, but try to replace part of your proof by sorry and see what happens. Of course this will add sorry as an axiom, but at some point choice should disappear. $\endgroup$
    – Ricky
    Commented Feb 18 at 11:28
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    $\begingroup$ I would even start by replacing the full proof by sorry, to check that the statement doesn't somehow uses choice. $\endgroup$
    – Ricky
    Commented Feb 18 at 11:29
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    $\begingroup$ I hate to say, this but the are many ways the axiom of choice can sneak into a Lean proof. Trying to do constructive math in Lean 4 is very painful. $\endgroup$
    – Jason Rute
    Commented Feb 18 at 12:29
  • $\begingroup$ Well, if you start using a lot of mathlib then I agree, but otherwise it should be more or less fine. $\endgroup$
    – Ricky
    Commented Feb 18 at 12:37
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    $\begingroup$ @Ricky. No. It is true in even base lean. Macros, automatic termination proofs, and common tactics can all add choice unexpectedly. $\endgroup$
    – Jason Rute
    Commented Feb 18 at 14:54