Goal:
  
  A : Type
  P : nat → A → Type
  k : nat
  a : A
  l : list A
  i : nat
  x : A
  h : P (k + S i) x
  IHl : ∀ k : nat,
          (∀ (i : nat) (x : A), nth_error l i = Some x → P (k + i) x)
          → Alli P k l
  H : nth_error l i = Some x
  ============================
   (P (k + S i) x)


DEBUG:Going to execute:
solve
[ trivial
with eq_true
| reflexivity
| symmetry; trivial
| contradiction
| congruence ]