Goal:
  
  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
  px : is_true (p x)
  pl : is_true (forallb p l)
  Hx : ∀ x : A, P x → p x → f x = g x
  ============================
   (∀ x : A, P x → p x → f x = g x)


DEBUG:Going to execute:
solve
[ trivial
with eq_true
| reflexivity
| symmetry; trivial
| contradiction
| congruence ]