Goal:
  
  A : Type
  H : ReflectEq A
  a1 : A
  l1 : list A
  a2 : A
  l2 : list A
  prefix : list A
  l1' : list A
  l2' : list A
  Heq : split_prefix l1 l2 = (prefix, l1', l2')
  Hind : ∀ (H := CoreTactics.block) (l3 l4 : list A),
           {| pr1 := l1; pr2 := l2 |} = {| pr1 := l3; pr2 := l4 |}
           → split_prefix l1 l2 = split_prefix l3 l4
             → let H0 := CoreTactics.block in
               let
               '(prefix, l1', l2') := split_prefix l3 l4 in
                l3 = prefix ++ l1' ∧ l4 = prefix ++ l2'
  Heq0 : (a1 == a2) = true
  ============================
   (∀ (H := CoreTactics.block) (l3 l4 : list A),
      {| pr1 := a1 :: l1; pr2 := a2 :: l2 |} = {| pr1 := l3; pr2 := l4 |}
      → (a1 :: prefix, l1', l2') = split_prefix l3 l4
        → let H0 := CoreTactics.block in
          let
          '(prefix, l1', l2') := split_prefix l3 l4 in
           l3 = prefix ++ l1' ∧ l4 = prefix ++ l2')


DEBUG:Going to execute:
intros _

Goals:
    A : Type  H : ReflectEq A  l2 : list A
  ============================
   (∀ l1 l3 : list A,
      {| pr1 := []; pr2 := l2 |} = {| pr1 := l1; pr2 := l3 |}
      → ([], [], l2) = split_prefix l1 l3
        → let H := CoreTactics.block in
          let
          '(prefix, l1', l2') := split_prefix l1 l3 in
           l1 = prefix ++ l1' ∧ l3 = prefix ++ l2')

    A : Type  H : ReflectEq A  a : A  l : list A
  ============================
   (∀ l1 l2 : list A,
      {| pr1 := a :: l; pr2 := [] |} = {| pr1 := l1; pr2 := l2 |}
      → ([], a :: l, []) = split_prefix l1 l2
        → let H := CoreTactics.block in
          let
          '(prefix, l1', l2') := split_prefix l1 l2 in
           l1 = prefix ++ l1' ∧ l2 = prefix ++ l2')

  
  A : Type
  H : ReflectEq A
  a1 : A
  l1 : list A
  a2 : A
  l2 : list A
  Heq : (a1 == a2) = false
  ============================
   (∀ l3 l4 : list A,
      {| pr1 := a1 :: l1; pr2 := a2 :: l2 |} = {| pr1 := l3; pr2 := l4 |}
      → ([], a1 :: l1, a2 :: l2) = split_prefix l3 l4
        → let H := CoreTactics.block in
          let
          '(prefix, l1', l2') := split_prefix l3 l4 in
           l3 = prefix ++ l1' ∧ l4 = prefix ++ l2')

  
  A : Type
  H : ReflectEq A
  a1 : A
  l1 : list A
  a2 : A
  l2 : list A
  prefix : list A
  l1' : list A
  l2' : list A
  Heq : split_prefix l1 l2 = (prefix, l1', l2')
  Hind : ∀ (H := CoreTactics.block) (l3 l4 : list A),
           {| pr1 := l1; pr2 := l2 |} = {| pr1 := l3; pr2 := l4 |}
           → split_prefix l1 l2 = split_prefix l3 l4
             → let H0 := CoreTactics.block in
               let
               '(prefix, l1', l2') := split_prefix l3 l4 in
                l3 = prefix ++ l1' ∧ l4 = prefix ++ l2'
  Heq0 : (a1 == a2) = true
  ============================
   (∀ l3 l4 : list A,
      {| pr1 := a1 :: l1; pr2 := a2 :: l2 |} = {| pr1 := l3; pr2 := l4 |}
      → (a1 :: prefix, l1', l2') = split_prefix l3 l4
        → let H := CoreTactics.block in
          let
          '(prefix, l1', l2') := split_prefix l3 l4 in
           l3 = prefix ++ l1' ∧ l4 = prefix ++ l2')


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
    A : Type  H : ReflectEq A  l2 : list A
  ============================
   (∀ l1 l3 : list A,
      {| pr1 := []; pr2 := l2 |} = {| pr1 := l1; pr2 := l3 |}
      → ([], [], l2) = split_prefix l1 l3
        → let H := CoreTactics.block in
          let
          '(prefix, l1', l2') := split_prefix l1 l3 in
           l1 = prefix ++ l1' ∧ l3 = prefix ++ l2')

    A : Type  H : ReflectEq A  a : A  l : list A
  ============================
   (∀ l1 l2 : list A,
      {| pr1 := a :: l; pr2 := [] |} = {| pr1 := l1; pr2 := l2 |}
      → ([], a :: l, []) = split_prefix l1 l2
        → let H := CoreTactics.block in
          let
          '(prefix, l1', l2') := split_prefix l1 l2 in
           l1 = prefix ++ l1' ∧ l2 = prefix ++ l2')

  
  A : Type
  H : ReflectEq A
  a1 : A
  l1 : list A
  a2 : A
  l2 : list A
  Heq : (a1 == a2) = false
  ============================
   (∀ l3 l4 : list A,
      {| pr1 := a1 :: l1; pr2 := a2 :: l2 |} = {| pr1 := l3; pr2 := l4 |}
      → ([], a1 :: l1, a2 :: l2) = split_prefix l3 l4
        → let H := CoreTactics.block in
          let
          '(prefix, l1', l2') := split_prefix l3 l4 in
           l3 = prefix ++ l1' ∧ l4 = prefix ++ l2')

  
  A : Type
  H : ReflectEq A
  a1 : A
  l1 : list A
  a2 : A
  l2 : list A
  prefix : list A
  l1' : list A
  l2' : list A
  Heq : split_prefix l1 l2 = (prefix, l1', l2')
  Hind : ∀ (H := CoreTactics.block) (l3 l4 : list A),
           {| pr1 := l1; pr2 := l2 |} = {| pr1 := l3; pr2 := l4 |}
           → split_prefix l1 l2 = split_prefix l3 l4
             → let H0 := CoreTactics.block in
               let
               '(prefix, l1', l2') := split_prefix l3 l4 in
                l3 = prefix ++ l1' ∧ l4 = prefix ++ l2'
  Heq0 : (a1 == a2) = true
  ============================
   (∀ l3 l4 : list A,
      {| pr1 := a1 :: l1; pr2 := a2 :: l2 |} = {| pr1 := l3; pr2 := l4 |}
      → (a1 :: prefix, l1', l2') = split_prefix l3 l4
        → let H := CoreTactics.block in
          let
          '(prefix, l1', l2') := split_prefix l3 l4 in
           l3 = prefix ++ l1' ∧ l4 = prefix ++ l2')


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim