Inductive eqP : list (Term A n) -> list (Term A n) -> Prop :=
  | eqP0 : eqP (pO A n) (pO A n)
  | eqpP1 :
      forall ma mb p q,
      eqTerm (A:=A) eqA (n:=n) ma mb -> eqP p q -> eqP (pX ma p) (pX mb q).Inductive eqP : list (Term A n) -> list (Term A n) -> Prop :=
  | eqP0 : eqP (pO A n) (pO A n)
  | eqpP1 :
      forall ma mb p q,
      eqTerm (A:=A) eqA (n:=n) ma mb -> eqP p q -> eqP (pX ma p) (pX mb q).Inductive eqP : list (Term A n) -> list (Term A n) -> Prop :=
  | eqP0 : eqP (pO A n) (pO A n)
  | eqpP1 :
      forall ma mb p q,
      eqTerm (A:=A) eqA (n:=n) ma mb -> eqP p q -> eqP (pX ma p) (pX mb q).

Lemma eqp_inv1 : forall p, eqP (pO A n) p -> p = pO A n.