Goal:
  
  G1 : t
  G2 : t
  H : invariants G1
  H0 : invariants G2
  H1 : acyclic_no_loop G2
  sub : subgraph G1 G2
  ext : is_true (is_full_extension G1 G2)
  ============================
   (forall v1 v2 : VSet.elt,
    VSet.In v1 (V G1) ->
    VSet.In v2 (V G1) -> (lsp G2 v1 v2 <= lsp G1 v1 v2)%nbar)


DEBUG:Going to execute:
trivial; hnf; intros; (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 ])