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')
  ============================
   ((∀ (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:
DepElim.simplify_one_dep_elim