This isn't just about good writing for math; the post author was trying to verify FLT as is developed in the literature, and along the way they discovered that a lemma underpinning a whole subfield is untrue, as was used. They nevertheless have confidence that the subfield is largely salvageable, by virtue of the faith that if it were bogus, someone would have already found negative results.

But now they had to find a suitable replacement to underpin the field.