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
  ============================
   (map_InP (x :: xs) (λ (x0 : A) (_ : In x0 (x :: xs)), f0 x0) =
    map f0 (x :: xs))


DEBUG:Going to execute:
case not_locked_false_eq_true; Ltac.assumption
Level 1: Backtrace:

In environment
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
Unable to unify "map f0 (x :: xs)" with
 "map_InP (x :: xs) (λ (x0 : A) (_ : In x0 (x :: xs)), f0 x0)".
Level 0: Backtrace:

In environment
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
Unable to unify "map f0 (x :: xs)" with
 "map_InP (x :: xs) (λ (x0 : A) (_ : In x0 (x :: xs)), f0 x0)".
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.