Goal:
  
  A : Type
  a : A
  l : list A
  IHl : ∀ n : nat, (∑ x : A, nth_error l n = Some x) <~> n < #|l|
  n : nat
  l0 : (∑ x : A, nth_error l n = Some x) → n < #|l|
  s : n < #|l| → ∑ x : A, nth_error l n = Some x
  X : ∑ x : A, nth_error l n = Some x
  ============================
   (S n < S #|l|)


DEBUG:Going to execute:
<coq-core.plugins.ltac::auto@0> $1 $2 $3