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
  H4 : InA E.eq x0 xs
  ============================
   (P x0)


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

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
  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
  H4 : InA E.eq x0 xs
  ============================
   (P x0)


DEBUG:Going to execute:
<Coq.Init.Tauto.not_dep_intros>

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
  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
  H4 : InA E.eq x0 xs
  ============================
   (P x0)


DEBUG:Going to execute:
repeat
            match goal with
            | |- ?X1 -> ?X2 => intro
            | |- ~ _ => unfold not at 1; intro
            end