Goal:
  
  G : t
  HI : invariants G
  HG : acyclic_no_loop G
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e : EdgeOf G x y
  p : SPath G s0 y z
  IHp : let H := CoreTactics.block in
        forall (x : V.t) (z0 : Z) (p0 : SPath G (V G) x (s G)),
        {|
          pr1 := {| pr1 := V G; pr2 := {| pr1 := x; pr2 := s G |} |};
          pr2 := p0
        |} =
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := y; pr2 := z |} |}; pr2 := p
        |} ->
        let H0 := CoreTactics.block in
        sweight p0 = z0 ->
        ~ VSet.In x (V G) -> let H1 := CoreTactics.block in z0 = 0
  ============================
   (let H := CoreTactics.block in
    forall (x0 : V.t) (z0 : Z) (p0 : SPath G (V G) x0 (s G)),
    {|
      pr1 := {| pr1 := V G; pr2 := {| pr1 := x0; pr2 := s G |} |}; pr2 := p0
    |} =
    {|
      pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
      pr2 := spath_step G s0 s' x y z d e p
    |} ->
    let H0 := CoreTactics.block in
    sweight p0 = z0 ->
    ~ VSet.In x0 (V G) -> let H1 := CoreTactics.block in z0 = 0)


DEBUG:Going to execute:
intros _

Goals:
    G : t  HI : invariants G  HG : acyclic_no_loop G  s0 : VSet.t  x : V.t
  ============================
   (forall (x0 : V.t) (z : Z) (p : SPath G (V G) x0 (s G)),
    {|
      pr1 := {| pr1 := V G; pr2 := {| pr1 := x0; pr2 := s G |} |}; pr2 := p
    |} =
    {|
      pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
      pr2 := spath_refl G s0 x
    |} ->
    let H := CoreTactics.block in
    sweight p = z ->
    ~ VSet.In x0 (V G) -> let H0 := CoreTactics.block in z = 0)

  
  G : t
  HI : invariants G
  HG : acyclic_no_loop G
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e : EdgeOf G x y
  p : SPath G s0 y z
  IHp : let H := CoreTactics.block in
        forall (x : V.t) (z0 : Z) (p0 : SPath G (V G) x (s G)),
        {|
          pr1 := {| pr1 := V G; pr2 := {| pr1 := x; pr2 := s G |} |};
          pr2 := p0
        |} =
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := y; pr2 := z |} |}; pr2 := p
        |} ->
        let H0 := CoreTactics.block in
        sweight p0 = z0 ->
        ~ VSet.In x (V G) -> let H1 := CoreTactics.block in z0 = 0
  ============================
   (forall (x0 : V.t) (z0 : Z) (p0 : SPath G (V G) x0 (s G)),
    {|
      pr1 := {| pr1 := V G; pr2 := {| pr1 := x0; pr2 := s G |} |}; pr2 := p0
    |} =
    {|
      pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
      pr2 := spath_step G s0 s' x y z d e p
    |} ->
    let H := CoreTactics.block in
    sweight p0 = z0 ->
    ~ VSet.In x0 (V G) -> let H0 := CoreTactics.block in z0 = 0)


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
    G : t  HI : invariants G  HG : acyclic_no_loop G  s0 : VSet.t  x : V.t
  ============================
   (forall (x0 : V.t) (z : Z) (p : SPath G (V G) x0 (s G)),
    {|
      pr1 := {| pr1 := V G; pr2 := {| pr1 := x0; pr2 := s G |} |}; pr2 := p
    |} =
    {|
      pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
      pr2 := spath_refl G s0 x
    |} ->
    let H := CoreTactics.block in
    sweight p = z ->
    ~ VSet.In x0 (V G) -> let H0 := CoreTactics.block in z = 0)

  
  G : t
  HI : invariants G
  HG : acyclic_no_loop G
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e : EdgeOf G x y
  p : SPath G s0 y z
  IHp : let H := CoreTactics.block in
        forall (x : V.t) (z0 : Z) (p0 : SPath G (V G) x (s G)),
        {|
          pr1 := {| pr1 := V G; pr2 := {| pr1 := x; pr2 := s G |} |};
          pr2 := p0
        |} =
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := y; pr2 := z |} |}; pr2 := p
        |} ->
        let H0 := CoreTactics.block in
        sweight p0 = z0 ->
        ~ VSet.In x (V G) -> let H1 := CoreTactics.block in z0 = 0
  ============================
   (forall (x0 : V.t) (z0 : Z) (p0 : SPath G (V G) x0 (s G)),
    {|
      pr1 := {| pr1 := V G; pr2 := {| pr1 := x0; pr2 := s G |} |}; pr2 := p0
    |} =
    {|
      pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
      pr2 := spath_step G s0 s' x y z d e p
    |} ->
    let H := CoreTactics.block in
    sweight p0 = z0 ->
    ~ VSet.In x0 (V G) -> let H0 := CoreTactics.block in z0 = 0)


DEBUG:Going to execute:
DepElim.simplify_dep_elim; DepElim.simplify_IH_hyps;
            DepElim.unblock_dep_elim

Goals:
    G : t  HI : invariants G  HG : acyclic_no_loop G  s0 : VSet.t  x : V.t
  ============================
   (forall (x0 : V.t) (z : Z) (p : SPath G (V G) x0 (s G)),
    {|
      pr1 := {| pr1 := V G; pr2 := {| pr1 := x0; pr2 := s G |} |}; pr2 := p
    |} =
    {|
      pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
      pr2 := spath_refl G s0 x
    |} ->
    let H := CoreTactics.block in
    sweight p = z ->
    ~ VSet.In x0 (V G) -> let H0 := CoreTactics.block in z = 0)

  
  G : t
  HI : invariants G
  HG : acyclic_no_loop G
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e : EdgeOf G x y
  p : SPath G s0 y z
  IHp : let H := CoreTactics.block in
        forall (x : V.t) (z0 : Z) (p0 : SPath G (V G) x (s G)),
        {|
          pr1 := {| pr1 := V G; pr2 := {| pr1 := x; pr2 := s G |} |};
          pr2 := p0
        |} =
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := y; pr2 := z |} |}; pr2 := p
        |} ->
        let H0 := CoreTactics.block in
        sweight p0 = z0 ->
        ~ VSet.In x (V G) -> let H1 := CoreTactics.block in z0 = 0
  ============================
   (forall (x0 : V.t) (z0 : Z) (p0 : SPath G (V G) x0 (s G)),
    {|
      pr1 := {| pr1 := V G; pr2 := {| pr1 := x0; pr2 := s G |} |}; pr2 := p0
    |} =
    {|
      pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
      pr2 := spath_step G s0 s' x y z d e p
    |} ->
    let H := CoreTactics.block in
    sweight p0 = z0 ->
    ~ VSet.In x0 (V G) -> let H0 := CoreTactics.block in z0 = 0)


DEBUG:Going to execute:
DepElim.simplify_dep_elim; DepElim.simplify_IH_hyps

Goals:
    G : t  HI : invariants G  HG : acyclic_no_loop G  s0 : VSet.t  x : V.t
  ============================
   (forall (x0 : V.t) (z : Z) (p : SPath G (V G) x0 (s G)),
    {|
      pr1 := {| pr1 := V G; pr2 := {| pr1 := x0; pr2 := s G |} |}; pr2 := p
    |} =
    {|
      pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
      pr2 := spath_refl G s0 x
    |} ->
    let H := CoreTactics.block in
    sweight p = z ->
    ~ VSet.In x0 (V G) -> let H0 := CoreTactics.block in z = 0)

  
  G : t
  HI : invariants G
  HG : acyclic_no_loop G
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e : EdgeOf G x y
  p : SPath G s0 y z
  IHp : let H := CoreTactics.block in
        forall (x : V.t) (z0 : Z) (p0 : SPath G (V G) x (s G)),
        {|
          pr1 := {| pr1 := V G; pr2 := {| pr1 := x; pr2 := s G |} |};
          pr2 := p0
        |} =
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := y; pr2 := z |} |}; pr2 := p
        |} ->
        let H0 := CoreTactics.block in
        sweight p0 = z0 ->
        ~ VSet.In x (V G) -> let H1 := CoreTactics.block in z0 = 0
  ============================
   (forall (x0 : V.t) (z0 : Z) (p0 : SPath G (V G) x0 (s G)),
    {|
      pr1 := {| pr1 := V G; pr2 := {| pr1 := x0; pr2 := s G |} |}; pr2 := p0
    |} =
    {|
      pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
      pr2 := spath_step G s0 s' x y z d e p
    |} ->
    let H := CoreTactics.block in
    sweight p0 = z0 ->
    ~ VSet.In x0 (V G) -> let H0 := CoreTactics.block in z0 = 0)


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
    G : t  HI : invariants G  HG : acyclic_no_loop G  s0 : VSet.t  x : V.t
  ============================
   (forall (x0 : V.t) (z : Z) (p : SPath G (V G) x0 (s G)),
    {|
      pr1 := {| pr1 := V G; pr2 := {| pr1 := x0; pr2 := s G |} |}; pr2 := p
    |} =
    {|
      pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
      pr2 := spath_refl G s0 x
    |} ->
    let H := CoreTactics.block in
    sweight p = z ->
    ~ VSet.In x0 (V G) -> let H0 := CoreTactics.block in z = 0)

  
  G : t
  HI : invariants G
  HG : acyclic_no_loop G
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e : EdgeOf G x y
  p : SPath G s0 y z
  IHp : let H := CoreTactics.block in
        forall (x : V.t) (z0 : Z) (p0 : SPath G (V G) x (s G)),
        {|
          pr1 := {| pr1 := V G; pr2 := {| pr1 := x; pr2 := s G |} |};
          pr2 := p0
        |} =
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := y; pr2 := z |} |}; pr2 := p
        |} ->
        let H0 := CoreTactics.block in
        sweight p0 = z0 ->
        ~ VSet.In x (V G) -> let H1 := CoreTactics.block in z0 = 0
  ============================
   (forall (x0 : V.t) (z0 : Z) (p0 : SPath G (V G) x0 (s G)),
    {|
      pr1 := {| pr1 := V G; pr2 := {| pr1 := x0; pr2 := s G |} |}; pr2 := p0
    |} =
    {|
      pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
      pr2 := spath_step G s0 s' x y z d e p
    |} ->
    let H := CoreTactics.block in
    sweight p0 = z0 ->
    ~ VSet.In x0 (V G) -> let H0 := CoreTactics.block in z0 = 0)


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim