Goal:
  
  A : Type
  B : Type
  P : nat → A → B → Type
  n : nat
  x : A
  c : B
  n0 : nat
  ============================
   (None = Some x → None = Some c → P (n0 + n) x c)


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 ])