Global Instance RelDec_string : RelDec (@eq string) :=
{| rel_dec := string_dec |}.
Global Instance RelDec_Correct_string : RelDec_Correct RelDec_string.
Global Instance Reflect_string_dec a b : Reflect (string_dec a b) (a = b) (a <> b).
Fixpoint string_cmp (l r : string) : comparison :=
match l , r with
| EmptyString , EmptyString => Eq
| EmptyString , _ => Lt
| _ , EmptyString => Gt
| String l ls , String r rs =>
ascii_cmp l r >> string_cmp ls rs
end.
Section Program_Scope.
Variable modulus : nat.
Hypothesis one_lt_mod : 1 < modulus.

Lemma _xxx : forall m n,
1 < m -> ~ n < m -> 0 < n.