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
  s0 : VSet.t
  s' : VSet.t
  z : V.t
  x0 : V.t
  z0 : Z
  t0 : V.t
  d : DisjointAdd (x0, z0, t0)..s s0 s'
  p : SPath Gl s0 (x0, z0, t0)..t z
  yin : VSet.In z (V G1)
  h : EdgeSet.In
        ((x0, z0, t0)..s, diff l (x0, z0, t0)..s (x0, z0, t0)..t,
         (x0, z0, t0)..t) (E Gl)
  IHp : VSet.In z (V G1) ->
        exists n : Z,
          lsp G2 (x0, z0, t0)..t (first_in G1 Gl p) = Some n /\
          sweight p <= n + diff l (first_in G1 Gl p) z
  e0G2 : EdgeSet.In (x0, z0, t0) (E G2)
  E : EdgeSet.In (x0, z0, t0) (E G1)
  ============================
   (exists n : Z,
      lsp G2 (x0, z0, t0)..s
        (first_in G1 Gl
           (spath_step Gl s0 s' (x0, z0, t0)..s (x0, z0, t0)..t z d
              (diff l (x0, z0, t0)..s (x0, z0, t0)..t; h) p)) = 
      Some n /\
      diff l (x0, z0, t0)..s (x0, z0, t0)..t + sweight p <=
      n +
      diff l
        (first_in G1 Gl
           (spath_step Gl s0 s' (x0, z0, t0)..s (x0, z0, t0)..t z d
              (diff l (x0, z0, t0)..s (x0, z0, t0)..t; h) p)) z)


DEBUG:Going to execute:
<coq-equations.plugin::simp@0> $1 $2
DEBUG LTAC Evaluated term: EdgeSet.mem_spec
DEBUG LTAC Evaluated term: e0