Goal:
  
  A : Type
  B : Type
  x : A
  xs : list A
  f0 : A → B
  H : ∀ f : A → B,
        (λ (x : A) (_ : In x xs), f0 x) = (λ (x : A) (_ : In x xs), f x)
        → map_InP xs (λ (x : A) (_ : In x xs), f0 x) = map f xs
  ============================
   ((λ (x : A) (_ : In x xs), f0 x) = λ (x : A) (_ : In x xs), f0 x)


DEBUG:Going to execute:
do_atom