Goal:
  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  y : B
  ys : list B
  ============================
   (∀ k : nat,
      All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k [] (y :: ys)
      → All2i R k [] [])


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 ])