Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  Pb : A → A → bool
  Γ : list A
  Δ : list A
  ============================
   (All2_fold (λ (_ _ : list A) (x x0 : A), Pb x x0) Γ Δ → forallb2 Pb Γ Δ)


DEBUG:Going to execute:
induction 1

Goals:
    A : Type  P : list A → list A → A → A → Type  Pb : A → A → bool
  ============================
   (is_true (forallb2 Pb [] []))

  
  A : Type
  P : list A → list A → A → A → Type
  Pb : A → A → bool
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold (λ (_ _ : list A) (x x0 : A), Pb x x0) Γ Γ'
  p : is_true (Pb d d')
  IHX : is_true (forallb2 Pb Γ Γ')
  ============================
   (is_true (forallb2 Pb (d :: Γ) (d' :: Γ')))


DEBUG:Going to execute:
simpl

Goals:
    A : Type  P : list A → list A → A → A → Type  Pb : A → A → bool
  ============================
   (is_true true)

  
  A : Type
  P : list A → list A → A → A → Type
  Pb : A → A → bool
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold (λ (_ _ : list A) (x x0 : A), Pb x x0) Γ Γ'
  p : is_true (Pb d d')
  IHX : is_true (forallb2 Pb Γ Γ')
  ============================
   (is_true (Pb d d' && forallb2 Pb Γ Γ'))


DEBUG:Going to execute:
auto

Goals:
    A : Type  P : list A → list A → A → A → Type  Pb : A → A → bool
  ============================
   (is_true true)

  
  A : Type
  P : list A → list A → A → A → Type
  Pb : A → A → bool
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold (λ (_ _ : list A) (x x0 : A), Pb x x0) Γ Γ'
  p : is_true (Pb d d')
  IHX : is_true (forallb2 Pb Γ Γ')
  ============================
   (is_true (Pb d d' && forallb2 Pb Γ Γ'))


DEBUG:Going to execute:
<coq-core.plugins.ltac::auto@0> $1 $2 $3

Goals:

DEBUG:Going to execute:
now rewrite p IHX

Goals:

DEBUG:Going to execute:
rewrite p IHX

Goals:

DEBUG:Going to execute:
t; easy

Goals:

DEBUG:Going to execute:
t

Goals:

DEBUG:Going to execute:
easy

Goals:

DEBUG:Going to execute:
easy0 || (solve [ intuition eauto  3 with core terms ])