refactor: simplify excluded middle proof #2625
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Marking as low priority. Lean has proof irrelevance. Thus, this commit does not benefit users. |
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The current
Classical.emproof isn't that easy to follow. Since Lean has quotients, we can take a two-element type likeBool, and quotient it byx = y ∨ P. Then, the surjectionBool → Asplits and we use the fact thatBoolhas decidable equality to decideP.Based on proof at https://ncatlab.org/nlab/show/Diaconescu-Goodman-Myhill+theorem.