feat(algebra/order): allow simp to flip inequalities #1418
Merged
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We have a constant problem that while
a > b
is definitionally equal tob < a
, tactics that work at the syntactic level can't see this.This change introduces two simp lemmas, rewriting
>
and≥
in terms of<
and≤
. This requires a few tweaks elsewhere (essentially places wheresimp
now finishes or comes closer to finishing).Later, I would like to
>
with<
in basic files.@[simp]
to many more lemmas about inequalities.well_founded
tactics, which actually break whensimp
is too good at inequalities. See feat(well_founded_tactics): patch default_dec_tac #1419.