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 l : list A),
           {| pr1 := l1; pr2 := l2 |} = {| pr1 := l3; pr2 := l4 |}
           → split_prefix l1 l2 = split_prefix l3 l4
             → let H0 := CoreTactics.block in
               is_prefix l l3
               → is_prefix l l4
                 → is_prefix l (fst (fst (split_prefix l3 l4)))
  Heq0 : (a1 == a2) = true
  ============================
   (∀ (H := CoreTactics.block) (l3 l4 l : 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
          is_prefix l l3
          → is_prefix l l4 → is_prefix l (fst (fst (split_prefix l3 l4))))


DEBUG:Going to execute:
intros _

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

    A : Type  H : ReflectEq A  a : A  l : list A
  ============================
   (∀ l1 l2 l0 : list A,
      {| pr1 := a :: l; pr2 := [] |} = {| pr1 := l1; pr2 := l2 |}
      → ([], a :: l, []) = split_prefix l1 l2
        → let H := CoreTactics.block in
          is_prefix l0 l1
          → is_prefix l0 l2 → is_prefix l0 (fst (fst (split_prefix l1 l2))))

  
  A : Type
  H : ReflectEq A
  a1 : A
  l1 : list A
  a2 : A
  l2 : list A
  Heq : (a1 == a2) = false
  ============================
   (∀ l3 l4 l : 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
          is_prefix l l3
          → is_prefix l l4 → is_prefix l (fst (fst (split_prefix l3 l4))))

  
  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 l : list A),
           {| pr1 := l1; pr2 := l2 |} = {| pr1 := l3; pr2 := l4 |}
           → split_prefix l1 l2 = split_prefix l3 l4
             → let H0 := CoreTactics.block in
               is_prefix l l3
               → is_prefix l l4
                 → is_prefix l (fst (fst (split_prefix l3 l4)))
  Heq0 : (a1 == a2) = true
  ============================
   (∀ l3 l4 l : 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
          is_prefix l l3
          → is_prefix l l4 → is_prefix l (fst (fst (split_prefix l3 l4))))


DEBUG:Going to execute:
DepElim.simplify_dep_elim

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

    A : Type  H : ReflectEq A  a : A  l : list A
  ============================
   (∀ l1 l2 l0 : list A,
      {| pr1 := a :: l; pr2 := [] |} = {| pr1 := l1; pr2 := l2 |}
      → ([], a :: l, []) = split_prefix l1 l2
        → let H := CoreTactics.block in
          is_prefix l0 l1
          → is_prefix l0 l2 → is_prefix l0 (fst (fst (split_prefix l1 l2))))

  
  A : Type
  H : ReflectEq A
  a1 : A
  l1 : list A
  a2 : A
  l2 : list A
  Heq : (a1 == a2) = false
  ============================
   (∀ l3 l4 l : 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
          is_prefix l l3
          → is_prefix l l4 → is_prefix l (fst (fst (split_prefix l3 l4))))

  
  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 l : list A),
           {| pr1 := l1; pr2 := l2 |} = {| pr1 := l3; pr2 := l4 |}
           → split_prefix l1 l2 = split_prefix l3 l4
             → let H0 := CoreTactics.block in
               is_prefix l l3
               → is_prefix l l4
                 → is_prefix l (fst (fst (split_prefix l3 l4)))
  Heq0 : (a1 == a2) = true
  ============================
   (∀ l3 l4 l : 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
          is_prefix l l3
          → is_prefix l l4 → is_prefix l (fst (fst (split_prefix l3 l4))))


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim