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
  ============================
   (R i x0 y0)


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

Goals:

DEBUG:Going to execute:
repeat (do_intro; try do_atom)

Goals:

DEBUG:Going to execute:
try arith_congr

Goals:

DEBUG:Going to execute:
solve [ split; do_ccl ]