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putnam_2023_a6: fix vacuous strategy-validity condition (Lean) and free-variable typo (Isabelle) - #369
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putnam_2023_a6: fix vacuous strategy-validity condition (Lean) and free-variable typo (Isabelle)#369AaronY77 wants to merge 2 commits into
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… 1..n The current condition `s g ∈ g` forces Bob to repeat a chosen number, so no legal game conforms and the statement is vacuous (trishullab#365).
`IsValidGame G` (free G) made the assumption contradictory (trishullab#365).
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Fixes #365.
IsValidStrategy s ↔ ∀ g, g.length > 0 → s g ∈ gforces Bob to repeat a chosen number, so no legal game of length ≥ 2 conforms and every valid strategy wins vacuously. The new condition requires, on every legal unfinished history, an unused number in1..n:IsWinningFor_defusesIsValidStrategy n s. Range and freshness are both needed (missing range was the Fix misformalizations #285 exploit). The statement elaborates on Lean v4.35.0 + current Mathlib; we have not proved the fixed theorem.IsValidGame G→IsValidGame ginIsValidGame_def(the freeGmade the assumptions contradictory). The Isabelle version still has no strategy-validity condition (see putnam_2023_a6 (Lean, Isabelle): statement is vacuous — "valid strategy" requires Bob to pick an already-chosen number #365); not changed here because we could not machine-check an Isabelle edit.