Goal:
  
  A : Type
  B : Type
  t' : A
  P : B → A → A → Type
  b : B
  bs : list B
  hd : A
  tl : list A
  p : P b hd t'
  e : #|bs| = #|tl|
  ============================
   (Some b = Some b × P b hd t')


DEBUG:Going to execute:
try do_atom; repeat (do_intro; try do_atom); try arith_congr;
            (solve [ split; do_ccl ])