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_In xs (λ (x : A) (_ : In x xs), f0 x) = map f xs
  ============================
   (map_In (x :: xs) (λ (x0 : A) (_ : In x0 (x :: xs)), f0 x0) =
    map f0 (x :: xs))


DEBUG:Going to execute:
do
![ solve
 [ trivial | apply : eq_sym ; trivial ]
 | discriminate
 | contradiction
 | Ltac.split ]