Goal:
  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    forall
      e : NoConfusion_SPath
            {|
              pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
              pr2 := spath_step d e0 a
            |}
            {|
              pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
              pr2 := b
            |},
    let H0 := CoreTactics.block in
    noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
simpl in H

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    forall
      e : NoConfusion_SPath
            {|
              pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
              pr2 := spath_refl s0 x
            |}
            {|
              pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
              pr2 := b
            |},
    let H0 := CoreTactics.block in
    noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    forall
      e : NoConfusion_SPath
            {|
              pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
              pr2 := spath_step d e0 a
            |}
            {|
              pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
              pr2 := b
            |},
    let H0 := CoreTactics.block in
    noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
DepElim.simplify_equations_in H

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    forall
      e : NoConfusion_SPath
            {|
              pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
              pr2 := spath_refl s0 x
            |}
            {|
              pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
              pr2 := b
            |},
    let H0 := CoreTactics.block in
    noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    forall
      e : NoConfusion_SPath
            {|
              pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
              pr2 := spath_step d e0 a
            |}
            {|
              pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
              pr2 := b
            |},
    let H0 := CoreTactics.block in
    noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
fun e =>
             repeat progress (autounfold with equations in e; simpl in e)

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    forall
      e : NoConfusion_SPath
            {|
              pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
              pr2 := spath_refl s0 x
            |}
            {|
              pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
              pr2 := b
            |},
    let H0 := CoreTactics.block in
    noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    forall
      e : NoConfusion_SPath
            {|
              pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
              pr2 := spath_step d e0 a
            |}
            {|
              pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
              pr2 := b
            |},
    let H0 := CoreTactics.block in
    noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
repeat progress (autounfold with equations in e; simpl in e)