Goal:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2All A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})


DEBUG:Going to execute:
simpl in H

Goals:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2All A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2All A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})


DEBUG:Going to execute:
DepElim.simplify_equations_in H

Goals:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2All A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2All A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})


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

Goals:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2All A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2All A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})


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