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)))
  ============================
   ((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:
simplify * || simplify ?; cbv beta