Goal:
  
  G1 : t
  G2 : t
  H : invariants G1
  ext := EdgeSet.diff (E G2) (E G1) : EdgeSet.t
  bs := border_set G1 ext : VSet.t
  H0 : invariants G2
  H1 : acyclic_no_loop G1
  H2 : acyclic_no_loop G2
  h : forall x y : VSet.elt,
      VSet.In x bs -> VSet.In y bs -> (lsp G2 x y <= lsp G1 x y)%nbar
  _s_ : VSet.t
  _x_ : V.t
  _Hyp_ : VSet.In _x_ (V G1)
  ============================
   (Some 0 <=
    lsp G2 _x_ (first_in G1 G2 (spath_refl G2 _s_ _x_)) +
    lsp G1 (first_in G1 G2 (spath_refl G2 _s_ _x_)) _x_)%nbar


DEBUG:Going to execute:
rewrite first_in_first // 2!lsp_xx //=