Goal:
  
  A : Type
  P : A → A → Type
  a : A
  l : list A
  f : A → A
  tl' : list A
  hp : ∀ x y : A, P (f x) y → ∑ y' : A, y = f y'
  IHl : ∀ l' : list A,
          OnOne2 P (map f l) l'
          → ∑ l'' : list A, OnOne2 (λ x y : A, P (f x) (f y)) l l''
  o : OnOne2 P (map f l) tl'
  x : list A
  o0 : OnOne2 (λ x y : A, P (f x) (f y)) l x
  ============================
   (OnOne2 (λ x y : A, P (f x) (f y)) l ?tl')


DEBUG:Going to execute:
contradiction
Level 1: Backtrace:

 The relation (OnOne2 (λ x y : A, P (f x) (f y))) is not a declared symmetric relation. Maybe you need to require the Coq.Classes.RelationClasses library
Level 0: Backtrace:

 The relation (OnOne2 (λ x y : A, P (f x) (f y))) is not a declared symmetric relation. Maybe you need to require the Coq.Classes.RelationClasses library
Level 0: Backtrace:

 The relation (OnOne2 (λ x y : A, P (f x) (f y))) is not a declared symmetric relation. Maybe you need to require the Coq.Classes.RelationClasses library