Goal:
  
  A : Type
  P : nat → A → Type
  f : nat → A → A
  n : nat
  hd : A
  tl : list A
  p : P n hd
  X : Alli P (S n) tl
  H : ∀ (n : nat) (x : A), P n x → f n x = x
  H0 : mapi_rec f tl (S n) = tl
  ============================
   (f n hd :: mapi_rec f tl (S n) = hd :: tl)


DEBUG:Going to execute:
<Coq.Init.Tauto.is_empty> flags X1; elim H
Level 2: Backtrace:

In environment
A : Type
P : nat → A → Type
f : nat → A → A
n : nat
hd : A
tl : list A
p : P n hd
X : Alli P (S n) tl
H : ∀ (n : nat) (x : A), P n x → f n x = x
H0 : mapi_rec f tl (S n) = tl
Unable to unify "hd :: tl" with "f n hd :: mapi_rec f tl (S n)".
Level 2: Backtrace:

In environment
A : Type
P : nat → A → Type
f : nat → A → A
n : nat
hd : A
tl : list A
p : P n hd
X : Alli P (S n) tl
H : ∀ (n : nat) (x : A), P n x → f n x = x
H0 : mapi_rec f tl (S n) = tl
Unable to unify "hd :: tl" with "f n hd :: mapi_rec f tl (S n)".
Level 3: Backtrace:

In environment
A : Type
P : nat → A → Type
f : nat → A → A
n : nat
hd : A
tl : list A
p : P n hd
X : Alli P (S n) tl
H : ∀ (n : nat) (x : A), P n x → f n x = x
H0 : mapi_rec f tl (S n) = tl
Unable to unify "hd :: tl" with "f n hd :: mapi_rec f tl (S n)".
Level 3: Backtrace:

In environment
A : Type
P : nat → A → Type
f : nat → A → A
n : nat
hd : A
tl : list A
p : P n hd
X : Alli P (S n) tl
H : ∀ (n : nat) (x : A), P n x → f n x = x
H0 : mapi_rec f tl (S n) = tl
Unable to unify "hd :: tl" with "f n hd :: mapi_rec f tl (S n)".
Level 2: Backtrace:

In environment
A : Type
P : nat → A → Type
f : nat → A → A
n : nat
hd : A
tl : list A
p : P n hd
X : Alli P (S n) tl
H : ∀ (n : nat) (x : A), P n x → f n x = x
H0 : mapi_rec f tl (S n) = tl
Unable to unify "hd :: tl" with "f n hd :: mapi_rec f tl (S n)".
Level 2: Backtrace:

In environment
A : Type
P : nat → A → Type
f : nat → A → A
n : nat
hd : A
tl : list A
p : P n hd
X : Alli P (S n) tl
H : ∀ (n : nat) (x : A), P n x → f n x = x
H0 : mapi_rec f tl (S n) = tl
Unable to unify "hd :: tl" with "f n hd :: mapi_rec f tl (S n)".