Definition Qpositive_as_well_ordering :=
  Build_well_ordering Qpositive bin_lt bin_eq bin_lt_is_order
    bin_eq_is_equality bin_lt_is_wf bin_lt_is_well_def_rht.

Lemma qlt_wf_rec_without_zeros_and_One : forall P : Z -> Z -> Z -> Z -> Qpositive -> Prop, (forall (a b c d : Z_pos) (p : Qpositive), (forall (r s t u : Z_pos) (p1 : Qpositive), qlt r s t u p1 a b c d p -> P r s t u p1) -> P a b c d p) -> forall (a b c d : Z_pos) (p : Qpositive), P a b c d p.