Module IndexedEqKind <: INDEXED_TYPE.
Definition t := equation_kind.
Definition index (x: t) :=
match x with Full => 1%positive | Low => 2%positive | High => 3%positive end.

Lemma index_inj: forall x y, index x = index y -> x = y.
Lemma lt_not_eq : forall x y : t, lt x y -> ~ eq x y.