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    $\begingroup$ All three examples are stated incorrectly. The first is trivially true. You are assuming what you are proving. The second you have the assumptions and the concluding reversed. The third is the same plus you have s and t. $\endgroup$
    – Jason Rute
    Commented Apr 13 at 12:22
  • $\begingroup$ I rewrote my answer below to tell you the correct way to write these. $\endgroup$
    – Jason Rute
    Commented Apr 14 at 14:22