Goal:
  
  A : Type
  B : Type
  P : B → A → A → Prop
  h : ∀ b : B, Transitive (P b)
  l'' : list A
  x : B
  y : A
  z : A
  l : list B
  l' : list A
  l''0 : list A
  H : P x y z
  hl : Forall3 P l l' l''0
  IHhl : ∀ l'' : list A, Forall3 P l l''0 l'' → Forall3 P l l' l''
  z0 : A
  l''1 : list A
  H0 : P x z z0
  H1 : Forall3 P l l''0 l''1
  ============================
   (P x y ?y)


DEBUG:Going to execute:
<Coq.Init.Tauto.simplif> flags
Level 3: evaluation returns
<Coq.Init.Tauto.simplif> flags;
 <Coq.Init.Tauto.axioms> flags ||
   match reverse goal with
   | id:(?X1 → ?X2) → ?X3
     |- _ =>
         Ltac.cut X3;
          [ intro; clear id; t_tauto_intuit
          | Ltac.cut (X1 → X2);
             [ exact
             id
             | generalize (λ y : X2, id (λ x : X1, y)); intro; clear id;
                (solve [ t_tauto_intuit ]) ] ]
   | id:¬ ?X1 → ?X3
     |- _ =>
         Ltac.cut X3;
          [ intro; clear id; t_tauto_intuit
          | Ltac.cut (¬ X1);
             [ exact id | clear id; intro; (solve [ t_tauto_intuit ]) ] ]
   | |- ?X1 =>
         <Coq.Init.Tauto.is_disj> flags X1; (solve
          [ Ltac.left; t_tauto_intuit | Ltac.right; t_tauto_intuit ])
   end ||
     match goal with
     | |- _ → _ => intro; t_tauto_intuit
     | |- _ => t_reduce; t_solver
     end || t_solver
where
t_tauto_intuit := <tactic closure>
of type
tacvalue
t_solver := eauto  3 with core terms
of type
tacvalue
t_reduce := <coq-core.plugins.tauto::reduction_not_iff@0>
of type
tacvalue
flags := 
of type
tauto_flags of type tacvalue

Level 2: evaluation returns
<Coq.Init.Tauto.simplif> flags;
 <Coq.Init.Tauto.axioms> flags ||
   match reverse goal with
   | id:(?X1 → ?X2) → ?X3
     |- _ =>
         Ltac.cut X3;
          [ intro; clear id; t_tauto_intuit
          | Ltac.cut (X1 → X2);
             [ exact
             id
             | generalize (λ y : X2, id (λ x : X1, y)); intro; clear id;
                (solve [ t_tauto_intuit ]) ] ]
   | id:¬ ?X1 → ?X3
     |- _ =>
         Ltac.cut X3;
          [ intro; clear id; t_tauto_intuit
          | Ltac.cut (¬ X1);
             [ exact id | clear id; intro; (solve [ t_tauto_intuit ]) ] ]
   | |- ?X1 =>
         <Coq.Init.Tauto.is_disj> flags X1; (solve
          [ Ltac.left; t_tauto_intuit | Ltac.right; t_tauto_intuit ])
   end ||
     match goal with
     | |- _ → _ => intro; t_tauto_intuit
     | |- _ => t_reduce; t_solver
     end || t_solver
where
t_tauto_intuit := <tactic closure>
of type
tacvalue
t_solver := eauto  3 with core terms
of type
tacvalue
t_reduce := <coq-core.plugins.tauto::reduction_not_iff@0>
of type
tacvalue
flags := 
of type
tauto_flags of type tacvalue

Level 1: evaluation returns
<Coq.Init.Tauto.simplif> flags;
 <Coq.Init.Tauto.axioms> flags ||
   match reverse goal with
   | id:(?X1 → ?X2) → ?X3
     |- _ =>
         Ltac.cut X3;
          [ intro; clear id; t_tauto_intuit
          | Ltac.cut (X1 → X2);
             [ exact
             id
             | generalize (λ y : X2, id (λ x : X1, y)); intro; clear id;
                (solve [ t_tauto_intuit ]) ] ]
   | id:¬ ?X1 → ?X3
     |- _ =>
         Ltac.cut X3;
          [ intro; clear id; t_tauto_intuit
          | Ltac.cut (¬ X1);
             [ exact id | clear id; intro; (solve [ t_tauto_intuit ]) ] ]
   | |- ?X1 =>
         <Coq.Init.Tauto.is_disj> flags X1; (solve
          [ Ltac.left; t_tauto_intuit | Ltac.right; t_tauto_intuit ])
   end ||
     match goal with
     | |- _ → _ => intro; t_tauto_intuit
     | |- _ => t_reduce; t_solver
     end || t_solver
where
t_tauto_intuit := <tactic closure>
of type
tacvalue
t_solver := eauto  3 with core terms
of type
tacvalue
t_reduce := <coq-core.plugins.tauto::reduction_not_iff@0>
of type
tacvalue
flags := 
of type
tauto_flags of type tacvalue