Definition Qpositive2_as_well_ordering :=
  Build_well_ordering Qpositive2 bin2_lt bin2_eq bin2_lt_is_order
    bin2_eq_is_equality bin2_lt_is_wf bin2_lt_is_well_def_rht.

(* Specifications: *)
Lemma octet_lt_wf_rec_without_zeros_and_One : forall P : Z -> Z -> Z -> Z -> Z -> Z -> Z -> Z -> Qpositive -> Qpositive -> Prop, (forall (a b c d e f g h : Z_pos) (q1 q2 : Qpositive), (forall (k l r s t u v w : Z_pos) (p1 p2 : Qpositive), octet_lt k l r s t u v w p1 p2 a b c d e f g h q1 q2 -> P k l r s t u v w p1 p2) -> P a b c d e f g h q1 q2) -> forall (a b c d e f g h : Z_pos) (q1 q2 : Qpositive), P a b c d e f g h q1 q2.
Lemma quadraticAcc_wf : forall (a b c d e f g h : Z) (p1 p2 : Qpositive), (0 < a + b + c + d)%Z -> (0 < e + f + g + h)%Z -> (0 <= a)%Z -> (0 <= b)%Z -> (0 <= c)%Z -> (0 <= d)%Z -> (0 <= e)%Z -> (0 <= f)%Z -> (0 <= g)%Z -> (0 <= h)%Z -> quadraticAcc a b c d e f g h p1 p2.