Goal:
    A : Type  l : list A  f : A → A
  ============================
   (All (λ x : A, f x = x) l → map f l = l)


DEBUG:Going to execute:
induction 1

Goals:
    A : Type  f : A → A
  ============================
   (map f [] = [])

  
  A : Type
  f : A → A
  x : A
  l : list A
  p : f x = x
  X : All (λ x : A, f x = x) l
  IHX : map f l = l
  ============================
   (map f (x :: l) = x :: l)


DEBUG:Going to execute:
simpl

Goals:
    A : Type  f : A → A
  ============================
   ([] = [])

  
  A : Type
  f : A → A
  x : A
  l : list A
  p : f x = x
  X : All (λ x : A, f x = x) l
  IHX : map f l = l
  ============================
   (f x :: map f l = x :: l)


DEBUG:Going to execute:
trivial

Goals:
    A : Type  f : A → A
  ============================
   ([] = [])

  
  A : Type
  f : A → A
  x : A
  l : list A
  p : f x = x
  X : All (λ x : A, f x = x) l
  IHX : map f l = l
  ============================
   (f x :: map f l = x :: l)


DEBUG:Going to execute:
<coq-core.plugins.ltac::trivial@0> $1 $2