Goal:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  IHa : All2i
          (λ (i : nat) (x : A) (y : B),
             (if i <? S n then False else nth_error l (i - S n) = Some x)
             × R i x y) (S n) l r
  i : nat
  x0 : A
  y0 : B
  ltb : ¬ i < S n
  e : nth_error l (i - S n) = Some x0
  r1 : R i x0 y0
  ltb' : ¬ i < n
  ============================
   (Some x0 = Some x0 × R i x0 y0)


DEBUG:Going to execute:
contradiction
Level 1: Backtrace:

 The relation prod is not a declared symmetric relation. Maybe you need to require the Coq.Classes.RelationClasses library
Level 0: Backtrace:

 The relation prod is not a declared symmetric relation. Maybe you need to require the Coq.Classes.RelationClasses library
Level 0: Backtrace:

 The relation prod is not a declared symmetric relation. Maybe you need to require the Coq.Classes.RelationClasses library