Goal:
  
  G1 : t
  G2 : t
  sub : full_subgraph G1 G2
  x : VSet.elt
  hx : VSet.In x (V G1)
  y : VSet.elt
  hy : VSet.In y (V G1)
  ============================
   (full_subgraph G1 G2)


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 ])