Goal:
  
  A : Type
  P : list A → A → Type
  Q : list A → A → Type
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : (∀ (Γ : list A) (x : A), P Γ x → Q Γ x) → All_fold Q Γ
  X0 : ∀ (Γ : list A) (x : A), P Γ x → Q Γ x
  ============================
   (All_fold Q (d :: Γ))


DEBUG:Going to execute:
match goal with
           | H:¬ _ |- _ => solve [ case H; trivial ]
           end
Level 1: Backtrace:

No such assumption.
Level 0: Backtrace:

No such assumption.
Level 0: Backtrace:

No such assumption.
Level 0: Backtrace:

No such assumption.

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → A → Type
  X : ∀ (Γ : list A) (x : A), P Γ x → Q Γ x
  ============================
   (All_fold Q [])

  
  A : Type
  P : list A → A → Type
  Q : list A → A → Type
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : (∀ (Γ : list A) (x : A), P Γ x → Q Γ x) → All_fold Q Γ
  X0 : ∀ (Γ : list A) (x : A), P Γ x → Q Γ x
  ============================
   (All_fold Q (d :: Γ))


DEBUG:Going to execute:
constructor
Level 0: Backtrace:

No matching clauses for match.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 1: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → A → Type
  X : ∀ (Γ : list A) (x : A), P Γ x → Q Γ x
  ============================
   (All_fold Q [])

  
  A : Type
  P : list A → A → Type
  Q : list A → A → Type
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : (∀ (Γ : list A) (x : A), P Γ x → Q Γ x) → All_fold Q Γ
  X0 : ∀ (Γ : list A) (x : A), P Γ x → Q Γ x
  ============================
   (All_fold Q (d :: Γ))


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

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → A → Type
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : (∀ (Γ : list A) (x : A), P Γ x → Q Γ x) → All_fold Q Γ
  X0 : ∀ (Γ : list A) (x : A), P Γ x → Q Γ x
  ============================
   (All_fold Q Γ)

  
  A : Type
  P : list A → A → Type
  Q : list A → A → Type
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : (∀ (Γ : list A) (x : A), P Γ x → Q Γ x) → All_fold Q Γ
  X0 : ∀ (Γ : list A) (x : A), P Γ x → Q Γ x
  ============================
   (Q Γ d)


DEBUG:Going to execute:
eauto

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → A → Type
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : (∀ (Γ : list A) (x : A), P Γ x → Q Γ x) → All_fold Q Γ
  X0 : ∀ (Γ : list A) (x : A), P Γ x → Q Γ x
  ============================
   (All_fold Q Γ)

  
  A : Type
  P : list A → A → Type
  Q : list A → A → Type
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : (∀ (Γ : list A) (x : A), P Γ x → Q Γ x) → All_fold Q Γ
  X0 : ∀ (Γ : list A) (x : A), P Γ x → Q Γ x
  ============================
   (Q Γ d)


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