Goal:
    A : Type  P : A → Prop  l : list A  H : ∀ x : A, In x l → P x
  ============================
   (Forall P l)


DEBUG:Going to execute:
induction l

Goals:
    A : Type  P : A → Prop  H : ∀ x : A, In x [] → P x
  ============================
   (Forall P [])

  
  A : Type
  P : A → Prop
  a : A
  l : list A
  H : ∀ x : A, In x (a :: l) → P x
  IHl : (∀ x : A, In x l → P x) → Forall P l
  ============================
   (Forall P (a :: l))


DEBUG:Going to execute:
constructor
DEBUG LTAC Evaluated term: l

Goals:
    A : Type  P : A → Prop  H : ∀ x : A, In x [] → P x
  ============================
   (Forall P [])

  
  A : Type
  P : A → Prop
  a : A
  l : list A
  H : ∀ x : A, In x (a :: l) → P x
  IHl : (∀ x : A, In x l → P x) → Forall P l
  ============================
   (Forall P (a :: l))


DEBUG:Going to execute:
<coq-core.plugins.ltac::constructor@0>

Goals:
  
  A : Type
  P : A → Prop
  a : A
  l : list A
  H : ∀ x : A, In x (a :: l) → P x
  IHl : (∀ x : A, In x l → P x) → Forall P l
  ============================
   (P a)

  
  A : Type
  P : A → Prop
  a : A
  l : list A
  H : ∀ x : A, In x (a :: l) → P x
  IHl : (∀ x : A, In x l → P x) → Forall P l
  ============================
   (Forall P l)


DEBUG:Going to execute:
auto

Goals:
  
  A : Type
  P : A → Prop
  a : A
  l : list A
  H : ∀ x : A, In x (a :: l) → P x
  IHl : (∀ x : A, In x l → P x) → Forall P l
  ============================
   (P a)

  
  A : Type
  P : A → Prop
  a : A
  l : list A
  H : ∀ x : A, In x (a :: l) → P x
  IHl : (∀ x : A, In x l → P x) → Forall P l
  ============================
   (Forall P l)


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