Goal:
  
  A : Type
  P : A → A → Type
  Q : A → Type
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : All Q tl → OnOne2 (λ x y : A, P x y × Q x) tl tl'
  X0 : Q hd
  X1 : All Q tl
  ============================
   (OnOne2 (λ x y : A, P x y × Q x) tl tl')


DEBUG:Going to execute:
match goal with
           | |- ?X1 → ?X2 => intro
           | |- ¬ _ => unfold not at 1; intro
           end
Level 0: Backtrace:

No matching clauses for match.

Goals:
  
  A : Type
  P : A → A → Type
  Q : A → Type
  hd : A
  tl : list A
  hd' : A
  p : P hd hd'
  X : Q hd
  X0 : All Q tl
  ============================
   (P hd hd' × Q hd)

  
  A : Type
  P : A → A → Type
  Q : A → Type
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : All Q tl → OnOne2 (λ x y : A, P x y × Q x) tl tl'
  X0 : Q hd
  X1 : All Q tl
  ============================
   (OnOne2 (λ x y : A, P x y × Q x) tl tl')


DEBUG:Going to execute:
repeat
            (match reverse goal with
             | id:?X1
               |- _ =>
                   <Coq.Init.Tauto.is_conj> flags X1; elim id; do 2 intro;
                    clear id
             | id:_ ↔ _ |- _ => elim id; do 2 intro; clear id
             | id:¬ _ |- _ => red in id
             | id:?X1
               |- _ =>
                   <Coq.Init.Tauto.is_disj> flags X1; elim id; intro; clear
                    id
             | _ =>
                 <Coq.Init.Tauto.find_cut>
                  ltac:(fun id0 id1 X2 =>
                          assert X2; [ exact (id0 id1) | clear id0 ])
             | id:?X1 → ?X2
               |- _ =>
                   <Coq.Init.Tauto.is_unit_or_eq> flags X1; Ltac.cut X2;
                    [ intro; clear id
                    | Ltac.cut X1; [ exact id | constructor 1; fail ] ]
             | id:?X1 → ?X2
               |- _ =>
                   <Coq.Init.Tauto.flatten_contravariant_conj> flags X1 X2 id
             | id:?X1 ↔ ?X2 → ?X3
               |- _ =>
                   assert ((X1 → X2) → (X2 → X1) → X3) by
                    (do 2 intro; apply id; Ltac.split; Ltac.assumption);
                    clear id
             | id:?X1 → ?X2
               |- _ =>
                   <Coq.Init.Tauto.flatten_contravariant_disj> flags X1 X2 id
             | |- ?X1 => <Coq.Init.Tauto.is_conj> flags X1; Ltac.split
             | |- _ ↔ _ => Ltac.split
             | |- ¬ _ => red
             end; <Coq.Init.Tauto.not_dep_intros>)
Level 0: Backtrace:

No matching clauses for match.