Goal:
  
  G1 : t
  G2 : t
  l : labelling
  Gl := relabel_on G1 G2 l : t
  H : invariants G1
  preserves_edges : forall e : EdgeSet.elt,
                    EdgeSet.In e (E G1) -> EdgeSet.In e (E G2)
  HGl : correct_labelling G1 l
  H0 : invariants G2
  H1 : acyclic_no_loop G2
  embed : forall v1 v2 : VSet.elt,
          VSet.In v1 (V G1) ->
          VSet.In v2 (V G1) -> (lsp G2 v1 v2 <= lsp G1 v1 v2)%nbar
  G : t
  a : sigma
        (fun index : sigma (fun _ : VSet.t => sigma (fun _ : V.t => V.t)) =>
         SPath G (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index)))
  ============================
   (Acc (SPath_subterm G) a)


DEBUG:Going to execute:
let tac2 H :=
            let ph := fresh "H" in
            let ph' := fresh "H" in
            destruct H as [H ph ph']
           in
           let tacT H := let ph := fresh "X" in
                         destruct H as [H ph] in
           let tacT2 H :=
            let ph := fresh "X" in
            let ph' := fresh "X" in
            destruct H as [H ph ph']
           in
           match goal with
           | H:exists y, _ y |- _ => tac H
           | H:{x : _ | ?P x} |- _ => tac H
           | H:∑ y, ?P y |- _ => tacT H
           | H:exists2 x : _, _ x & _ x |- _ => tac2 H
           | H:{x : _ | ?P x & _ x} |- _ => tac2 H
           | H:{x : _ & ?P x & _ x} |- _ => tacT2 H
           end