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refactor: simplify excluded middle proof

Open james-smith-a8e6 opened this issue 2 years ago • 1 comments

The current Classical.em proof isn't that easy to follow. Since Lean has quotients, we can take a two-element type like Bool, and quotient it by x = y ∨ P. Then, the surjection Bool → A splits and we use the fact that Bool has decidable equality to decide P.

Based on proof at https://ncatlab.org/nlab/show/Diaconescu-Goodman-Myhill+theorem.

james-smith-a8e6 avatar Oct 05 '23 05:10 james-smith-a8e6

Marking as low priority. Lean has proof irrelevance. Thus, this commit does not benefit users.

leodemoura avatar Oct 09 '23 00:10 leodemoura