Goal:
  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : R x y
  rs : All2 R l l'
  r0 : R' x y r
  a0 : All2_dep R' rs
  b : All2_dep R' (All2_cons r rs)
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' 
                                      (x :: l) (y :: l') 
                                      (All2_cons r rs) 
                                      (All2_dep_cons r0 a0) b),
      let H0 := CoreTactics.block in
      noConfusionHom_All2_dep_obligation_2 A B R R' 
        (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b
        (noConfusionHom_All2_dep_obligation_1 A B R R' 
           (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b e) = e)


DEBUG:Going to execute:
simpl in H

Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  b : All2_dep R' All2_nil
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' [] []
                                      All2_nil All2_dep_nil b),
      let H0 := CoreTactics.block in
      noConfusionHom_All2_dep_obligation_2 A B R R' [] [] All2_nil
        All2_dep_nil b
        (noConfusionHom_All2_dep_obligation_1 A B R R' [] [] All2_nil
           All2_dep_nil b e) = e)

  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : R x y
  rs : All2 R l l'
  r0 : R' x y r
  a0 : All2_dep R' rs
  b : All2_dep R' (All2_cons r rs)
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' 
                                      (x :: l) (y :: l') 
                                      (All2_cons r rs) 
                                      (All2_dep_cons r0 a0) b),
      let H0 := CoreTactics.block in
      noConfusionHom_All2_dep_obligation_2 A B R R' 
        (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b
        (noConfusionHom_All2_dep_obligation_1 A B R R' 
           (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b e) = e)


DEBUG:Going to execute:
DepElim.simplify_equations_in H

Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  b : All2_dep R' All2_nil
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' [] []
                                      All2_nil All2_dep_nil b),
      let H0 := CoreTactics.block in
      noConfusionHom_All2_dep_obligation_2 A B R R' [] [] All2_nil
        All2_dep_nil b
        (noConfusionHom_All2_dep_obligation_1 A B R R' [] [] All2_nil
           All2_dep_nil b e) = e)

  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : R x y
  rs : All2 R l l'
  r0 : R' x y r
  a0 : All2_dep R' rs
  b : All2_dep R' (All2_cons r rs)
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' 
                                      (x :: l) (y :: l') 
                                      (All2_cons r rs) 
                                      (All2_dep_cons r0 a0) b),
      let H0 := CoreTactics.block in
      noConfusionHom_All2_dep_obligation_2 A B R R' 
        (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b
        (noConfusionHom_All2_dep_obligation_1 A B R R' 
           (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b e) = e)


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

Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  b : All2_dep R' All2_nil
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' [] []
                                      All2_nil All2_dep_nil b),
      let H0 := CoreTactics.block in
      noConfusionHom_All2_dep_obligation_2 A B R R' [] [] All2_nil
        All2_dep_nil b
        (noConfusionHom_All2_dep_obligation_1 A B R R' [] [] All2_nil
           All2_dep_nil b e) = e)

  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : R x y
  rs : All2 R l l'
  r0 : R' x y r
  a0 : All2_dep R' rs
  b : All2_dep R' (All2_cons r rs)
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' 
                                      (x :: l) (y :: l') 
                                      (All2_cons r rs) 
                                      (All2_dep_cons r0 a0) b),
      let H0 := CoreTactics.block in
      noConfusionHom_All2_dep_obligation_2 A B R R' 
        (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b
        (noConfusionHom_All2_dep_obligation_1 A B R R' 
           (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b e) = e)


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