English
Under LT, comparing toDual flips the order: Compares o (toDual a) (toDual b) iff Compares o b a.
Русский
В линейном порядке, сопоставляя через toDual, порядок разворачивается: Compares o (toDual a) (toDual b) эквивалентно Compares o b a.
LaTeX
$$$\\forall o\\ a\\ b,\\ Compares o (toDual a) (toDual b) \\leftrightarrow Compares o b a$$$
Lean4
@[simp]
theorem toDual_compares_toDual [LT α] {a b : α} {o : Ordering} : Compares o (toDual a) (toDual b) ↔ Compares o b a :=
by
cases o
exacts [Iff.rfl, eq_comm, Iff.rfl]