Goal:
  
  P : E.t -> Prop
  P_Proper : Proper (E.eq ==> impl) P
  s : t
  x : elt
  xs : list elt
  H2 : P x
  H3 : forall x : elt, InA E.eq x xs -> P x
  H1 : Forall P xs
  H0 : forall x : elt, InA E.eq x xs -> P x
  x0 : elt
  H : E.eq x0 x \/ InA E.eq x0 xs
  ============================
   (P x0)


DEBUG:Going to execute:
elim id
Level 3: evaluation returns
<coq-core.plugins.tauto::is_disj@0>
where
tauto_flags := 
of type
tauto_flags
X1 := E.eq x0 x \/ InA E.eq x0 xs
of type
constr of type tacvalue


Goals:
  
  P : E.t -> Prop
  P_Proper : Proper (E.eq ==> impl) P
  s : t
  x : elt
  xs : list elt
  H2 : P x
  H3 : forall x : elt, InA E.eq x xs -> P x
  H1 : Forall P xs
  H0 : forall x : elt, InA E.eq x xs -> P x
  x0 : elt
  H : E.eq x0 x \/ InA E.eq x0 xs
  ============================
   (E.eq x0 x -> P x0)

  
  P : E.t -> Prop
  P_Proper : Proper (E.eq ==> impl) P
  s : t
  x : elt
  xs : list elt
  H2 : P x
  H3 : forall x : elt, InA E.eq x xs -> P x
  H1 : Forall P xs
  H0 : forall x : elt, InA E.eq x xs -> P x
  x0 : elt
  H : E.eq x0 x \/ InA E.eq x0 xs
  ============================
   (InA E.eq x0 xs -> P x0)


DEBUG:Going to execute:
intro
DEBUG LTAC Evaluated term: H

Goals:
  
  P : E.t -> Prop
  P_Proper : Proper (E.eq ==> impl) P
  s : t
  x : elt
  xs : list elt
  H2 : P x
  H3 : forall x : elt, InA E.eq x xs -> P x
  H1 : Forall P xs
  H0 : forall x : elt, InA E.eq x xs -> P x
  x0 : elt
  H : E.eq x0 x \/ InA E.eq x0 xs
  ============================
   (E.eq x0 x -> P x0)

  
  P : E.t -> Prop
  P_Proper : Proper (E.eq ==> impl) P
  s : t
  x : elt
  xs : list elt
  H2 : P x
  H3 : forall x : elt, InA E.eq x xs -> P x
  H1 : Forall P xs
  H0 : forall x : elt, InA E.eq x xs -> P x
  x0 : elt
  H : E.eq x0 x \/ InA E.eq x0 xs
  ============================
   (InA E.eq x0 xs -> P x0)


DEBUG:Going to execute:
<coq-core.plugins.ltac::intro@0>

Goals:
  
  P : E.t -> Prop
  P_Proper : Proper (E.eq ==> impl) P
  s : t
  x : elt
  xs : list elt
  H2 : P x
  H3 : forall x : elt, InA E.eq x xs -> P x
  H1 : Forall P xs
  H0 : forall x : elt, InA E.eq x xs -> P x
  x0 : elt
  H : E.eq x0 x \/ InA E.eq x0 xs
  H4 : E.eq x0 x
  ============================
   (P x0)

  
  P : E.t -> Prop
  P_Proper : Proper (E.eq ==> impl) P
  s : t
  x : elt
  xs : list elt
  H2 : P x
  H3 : forall x : elt, InA E.eq x xs -> P x
  H1 : Forall P xs
  H0 : forall x : elt, InA E.eq x xs -> P x
  x0 : elt
  H : E.eq x0 x \/ InA E.eq x0 xs
  H4 : InA E.eq x0 xs
  ============================
   (P x0)


DEBUG:Going to execute:
clear id