Module string_lex_as_OT_compat <: UsualOrderedType.
Definition t := string.
Definition eq := @eq string.
Definition lt := lex_lt.
Definition eq_refl := @eq_refl string.
Definition eq_sym := @eq_sym string.
Definition eq_trans := @eq_trans string.
Definition lt_trans := lex_lt_trans.
Definition lt_not_eq := lex_lt_not_eq.
Definition compare := string_compare_lex_compat.
Definition eq_dec := string_dec.
End string_lex_as_OT_compat.

Theorem lex_lt_lt_compat : Proper (eq ==> eq ==> iff) lex_lt.