Section EqPath.
Variables (n0 : nat) (T : eqType) (e : rel T).
Implicit Type p : seq T.
Variant split x : seq T -> seq T -> seq T -> Type :=
Split p1 p2 : split x (rcons p1 x ++ p2) p1 p2.
Variant splitr x : seq T -> Type :=
Splitr p1 p2 : splitr x (p1 ++ x :: p2).

Lemma mem_next p x : (next p x \in p) = (x \in p).