Goal:
  
  G : t
  z : V.t
  x : V.t
  y : V.t
  z0 : V.t
  e : EdgeOf x y
  p : PathOf y z0
  q : PathOf z0 z
  IHp : weight (concat p q) = weight p + weight q
  ============================
   (e.π1 + weight (concat p q) = e.π1 + weight p + weight q)


DEBUG:Going to execute:
match reverse goal with
           | id:?X1
             |- _ =>
                 <Coq.Init.Tauto.is_conj> flags X1; elim id; do 2 intro;
                  clear id
           | id:_ <-> _ |- _ => elim id; do 2 intro; clear id
           | id:~ _ |- _ => red in id
           | id:?X1
             |- _ =>
                 <Coq.Init.Tauto.is_disj> flags X1; elim id; intro; clear id
           | _ =>
               <Coq.Init.Tauto.find_cut>
                ltac:(fun id0 id1 X2 =>
                        assert X2; [ exact (id0 id1) | clear id0 ])
           | id:?X1 -> ?X2
             |- _ =>
                 <Coq.Init.Tauto.is_unit_or_eq> flags X1; Ltac.cut X2;
                  [ intro; clear id
                  | Ltac.cut X1; [ exact id | constructor 1; fail ] ]
           | id:?X1 -> ?X2
             |- _ =>
                 <Coq.Init.Tauto.flatten_contravariant_conj> flags X1 X2 id
           | id:?X1 <-> ?X2 -> ?X3
             |- _ =>
                 assert ((X1 -> X2) -> (X2 -> X1) -> X3) by
                  (do 2 intro; apply id; Ltac.split; Ltac.assumption); clear
                  id
           | id:?X1 -> ?X2
             |- _ =>
                 <Coq.Init.Tauto.flatten_contravariant_disj> flags X1 X2 id
           | |- ?X1 => <Coq.Init.Tauto.is_conj> flags X1; Ltac.split
           | |- _ <-> _ => Ltac.split
           | |- ~ _ => red
           end; <Coq.Init.Tauto.not_dep_intros>