Goal:
  
  A : Type
  B : Type
  P : A → Type
  p : A → bool
  l : list A
  f : A → B
  g : A → B
  ============================
   (All P l
    → forallb p l → (∀ x : A, P x → p x → f x = g x) → map f l = map g l)


DEBUG:Going to execute:
induction 1

Goals:
    A : Type  B : Type  P : A → Type  p : A → bool  f : A → B  g : A → B
  ============================
   (forallb p [] → (∀ x : A, P x → p x → f x = g x) → map f [] = map g [])

  
  A : Type
  B : Type
  P : A → Type
  p : A → bool
  f : A → B
  g : A → B
  x : A
  l : list A
  p0 : P x
  X : All P l
  IHX : forallb p l → (∀ x : A, P x → p x → f x = g x) → map f l = map g l
  ============================
   (forallb p (x :: l)
    → (∀ x : A, P x → p x → f x = g x) → map f (x :: l) = map g (x :: l))


DEBUG:Going to execute:
simpl

Goals:
    A : Type  B : Type  P : A → Type  p : A → bool  f : A → B  g : A → B
  ============================
   (true → (∀ x : A, P x → p x → f x = g x) → [] = [])

  
  A : Type
  B : Type
  P : A → Type
  p : A → bool
  f : A → B
  g : A → B
  x : A
  l : list A
  p0 : P x
  X : All P l
  IHX : forallb p l → (∀ x : A, P x → p x → f x = g x) → map f l = map g l
  ============================
   (p x && forallb p l
    → (∀ x : A, P x → p x → f x = g x) → f x :: map f l = g x :: map g l)


DEBUG:Going to execute:
trivial

Goals:
    A : Type  B : Type  P : A → Type  p : A → bool  f : A → B  g : A → B
  ============================
   (true → (∀ x : A, P x → p x → f x = g x) → [] = [])

  
  A : Type
  B : Type
  P : A → Type
  p : A → bool
  f : A → B
  g : A → B
  x : A
  l : list A
  p0 : P x
  X : All P l
  IHX : forallb p l → (∀ x : A, P x → p x → f x = g x) → map f l = map g l
  ============================
   (p x && forallb p l
    → (∀ x : A, P x → p x → f x = g x) → f x :: map f l = g x :: map g l)


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