Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  idx2 : list A
  idx1 : list A
  b : All2_fold P idx2 idx1
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} = {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |})


DEBUG:Going to execute:
simpl in H

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  idx2 : list A
  idx1 : list A
  b : All2_fold P idx2 idx1
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
    → let H0 := CoreTactics.block in
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |} =
      {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  idx2 : list A
  idx1 : list A
  b : All2_fold P idx2 idx1
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} = {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |})


DEBUG:Going to execute:
DepElim.simplify_equations_in H

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  idx2 : list A
  idx1 : list A
  b : All2_fold P idx2 idx1
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
    → let H0 := CoreTactics.block in
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |} =
      {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  idx2 : list A
  idx1 : list A
  b : All2_fold P idx2 idx1
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} = {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |})


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

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  idx2 : list A
  idx1 : list A
  b : All2_fold P idx2 idx1
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
    → let H0 := CoreTactics.block in
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |} =
      {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  idx2 : list A
  idx1 : list A
  b : All2_fold P idx2 idx1
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} = {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |})


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