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
  x : VSet.elt
  y : VSet.elt
  hx : VSet.In x (V G1)
  hy : VSet.In y (V G1)
  _a_ : Z
  p : SPath G2 (V G2) x y
  hp : sweight p = _a_
  ============================
   (VSet.In x (V G1))


DEBUG:Going to execute:
<coq-core.plugins.ltac::trivial@0> $1 $2

Goals:

DEBUG:Going to execute:
hnf

Goals:

DEBUG:Going to execute:
intros

Goals:

DEBUG:Going to execute:
solve
[ do
![ solve
 [ trivial | apply : eq_sym ; trivial ]
 | discriminate
 | contradiction
 | Ltac.split ]
| case not_locked_false_eq_true; Ltac.assumption
| match goal with
  | H:~ _ |- _ => solve [ case H; trivial ]
  end ]