Goal:
  
  A : Type
  l' : list A
  a0 : A
  r' : list A
  H0 : #|a0 :: r'| = #|a0 :: r'|
  H : (l' ++ [a0]) ++ r' = (l' ++ [a0]) ++ r'
  IHr : ∀ l l' r'0 : list A,
          l ++ r' = l' ++ r'0 → #|r'| = #|r'0| → l = l' ∧ r' = r'0
  ============================
   (l' = l' ∧ a0 :: r' = a0 :: r')


DEBUG:Going to execute:
fun => <coq-core.plugins.ltac::split@0>

Goals:
  
  A : Type
  l' : list A
  a0 : A
  r' : list A
  H0 : #|a0 :: r'| = #|a0 :: r'|
  H : (l' ++ [a0]) ++ r' = (l' ++ [a0]) ++ r'
  IHr : ∀ l l' r'0 : list A,
          l ++ r' = l' ++ r'0 → #|r'| = #|r'0| → l = l' ∧ r' = r'0
  ============================
   (l' = l')

  
  A : Type
  l' : list A
  a0 : A
  r' : list A
  H0 : #|a0 :: r'| = #|a0 :: r'|
  H : (l' ++ [a0]) ++ r' = (l' ++ [a0]) ++ r'
  IHr : ∀ l l' r'0 : list A,
          l ++ r' = l' ++ r'0 → #|r'| = #|r'0| → l = l' ∧ r' = r'0
  ============================
   (a0 :: r' = a0 :: r')


DEBUG:Going to execute:
do_ccl

Goals:
  
  A : Type
  l' : list A
  a0 : A
  r' : list A
  H0 : #|a0 :: r'| = #|a0 :: r'|
  H : (l' ++ [a0]) ++ r' = (l' ++ [a0]) ++ r'
  IHr : ∀ l l' r'0 : list A,
          l ++ r' = l' ++ r'0 → #|r'| = #|r'0| → l = l' ∧ r' = r'0
  ============================
   (l' = l')

  
  A : Type
  l' : list A
  a0 : A
  r' : list A
  H0 : #|a0 :: r'| = #|a0 :: r'|
  H : (l' ++ [a0]) ++ r' = (l' ++ [a0]) ++ r'
  IHr : ∀ l l' r'0 : list A,
          l ++ r' = l' ++ r'0 → #|r'| = #|r'0| → l = l' ∧ r' = r'0
  ============================
   (a0 :: r' = a0 :: r')


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

Goals:
  
  A : Type
  l' : list A
  a0 : A
  r' : list A
  H0 : #|a0 :: r'| = #|a0 :: r'|
  H : (l' ++ [a0]) ++ r' = (l' ++ [a0]) ++ r'
  IHr : ∀ l l' r'0 : list A,
          l ++ r' = l' ++ r'0 → #|r'| = #|r'0| → l = l' ∧ r' = r'0
  ============================
   (l' = l')

  
  A : Type
  l' : list A
  a0 : A
  r' : list A
  H0 : #|a0 :: r'| = #|a0 :: r'|
  H : (l' ++ [a0]) ++ r' = (l' ++ [a0]) ++ r'
  IHr : ∀ l l' r'0 : list A,
          l ++ r' = l' ++ r'0 → #|r'| = #|r'0| → l = l' ∧ r' = r'0
  ============================
   (a0 :: r' = a0 :: r')


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

Goals:
  
  A : Type
  l' : list A
  a0 : A
  r' : list A
  H0 : #|a0 :: r'| = #|a0 :: r'|
  H : (l' ++ [a0]) ++ r' = (l' ++ [a0]) ++ r'
  IHr : ∀ l l' r'0 : list A,
          l ++ r' = l' ++ r'0 → #|r'| = #|r'0| → l = l' ∧ r' = r'0
  ============================
   (l' = l')

  
  A : Type
  l' : list A
  a0 : A
  r' : list A
  H0 : #|a0 :: r'| = #|a0 :: r'|
  H : (l' ++ [a0]) ++ r' = (l' ++ [a0]) ++ r'
  IHr : ∀ l l' r'0 : list A,
          l ++ r' = l' ++ r'0 → #|r'| = #|r'0| → l = l' ∧ r' = r'0
  ============================
   (a0 :: r' = a0 :: r')


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

Goals:
  
  A : Type
  l' : list A
  a0 : A
  r' : list A
  H0 : #|a0 :: r'| = #|a0 :: r'|
  H : (l' ++ [a0]) ++ r' = (l' ++ [a0]) ++ r'
  IHr : ∀ l l' r'0 : list A,
          l ++ r' = l' ++ r'0 → #|r'| = #|r'0| → l = l' ∧ r' = r'0
  ============================
   (l' = l')

  
  A : Type
  l' : list A
  a0 : A
  r' : list A
  H0 : #|a0 :: r'| = #|a0 :: r'|
  H : (l' ++ [a0]) ++ r' = (l' ++ [a0]) ++ r'
  IHr : ∀ l l' r'0 : list A,
          l ++ r' = l' ++ r'0 → #|r'| = #|r'0| → l = l' ∧ r' = r'0
  ============================
   (a0 :: r' = a0 :: r')


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

Goals:
  
  A : Type
  l' : list A
  a0 : A
  r' : list A
  H0 : #|a0 :: r'| = #|a0 :: r'|
  H : (l' ++ [a0]) ++ r' = (l' ++ [a0]) ++ r'
  IHr : ∀ l l' r'0 : list A,
          l ++ r' = l' ++ r'0 → #|r'| = #|r'0| → l = l' ∧ r' = r'0
  ============================
   (l' = l')

  
  A : Type
  l' : list A
  a0 : A
  r' : list A
  H0 : #|a0 :: r'| = #|a0 :: r'|
  H : (l' ++ [a0]) ++ r' = (l' ++ [a0]) ++ r'
  IHr : ∀ l l' r'0 : list A,
          l ++ r' = l' ++ r'0 → #|r'| = #|r'0| → l = l' ∧ r' = r'0
  ============================
   (a0 :: r' = a0 :: r')


DEBUG:Going to execute:
try do_atom