Definition ltb (s1 s2 : string) : bool :=
if compare s1 s2 is Lt then true else false.
Definition leb (s1 s2 : string) : bool :=
if compare s1 s2 is Gt then false else true.

Lemma leb_antisym (s1 s2 : string) :
leb s1 s2 = true -> leb s2 s1 = true -> s1 = s2.