Section Walk_finds_Path.
Hypothesis In_dec : forall v : V, forall vs : list V, In v vs \/ ~ In v vs.
End Walk_finds_Path.
Definition trail (v' : V) (v : V) (vs : list V) : Prop :=
v ~~~[ vs ]~~> v' /\ NoDup (L.mk_edge_seq v vs).
#[local] Notation " src ===[ t ]==> tgt " := (trail tgt src t) : type_scope.

Lemma path_implies_trail (v0 : V) (v : V) (p : list V)
(PATH : v0 ---[ p ]--> v)
: v0 ===[ p ]==> v.