Instance paco5_inst  T0 T1 T2 T3 T4 (gf : rel5 T0 T1 T2 T3 T4->_) r x0 x1 x2 x3 x4 : paco_class (paco5 gf r x0 x1 x2 x3 x4) :=
{ pacoacc    := paco5_acc gf;
  pacomult   := paco5_mult gf;
  pacofold   := paco5_fold gf;
  pacounfold := paco5_unfold gf }.Definition monotone5_2 T0 T1 T2 T3 T4 (gf: rel5 T0 T1 T2 T3 T4 -> rel5 T0 T1 T2 T3 T4 -> rel5 T0 T1 T2 T3 T4) :=
  forall x0 x1 x2 x3 x4 r_0 r_1 r'_0 r'_1 (IN: gf r_0 r_1 x0 x1 x2 x3 x4) (LE_0: r_0 <5= r'_0)(LE_1: r_1 <5= r'_1), gf r'_0 r'_1 x0 x1 x2 x3 x4.

(* Specifications: *)
Theorem paco5_2_0_acc: forall l r_0 r_1 (OBG: forall rr (INC: r_0 <5= rr) (CIH: l <_paco_5= rr), l <_paco_5= paco5_2_0 gf_0 gf_1 rr r_1), l <5= paco5_2_0 gf_0 gf_1 r_0 r_1.
Theorem paco5_2_1_acc: forall l r_0 r_1 (OBG: forall rr (INC: r_1 <5= rr) (CIH: l <_paco_5= rr), l <_paco_5= paco5_2_1 gf_0 gf_1 r_0 rr), l <5= paco5_2_1 gf_0 gf_1 r_0 r_1.
Theorem paco5_2_0_mon: monotone5_2 (paco5_2_0 gf_0 gf_1).
Theorem paco5_2_1_mon: monotone5_2 (paco5_2_1 gf_0 gf_1).
Theorem paco5_2_0_mult_strong: forall r_0 r_1, paco5_2_0 gf_0 gf_1 (upaco5_2_0 gf_0 gf_1 r_0 r_1) (upaco5_2_1 gf_0 gf_1 r_0 r_1) <5= paco5_2_0 gf_0 gf_1 r_0 r_1.
Theorem paco5_2_1_mult_strong: forall r_0 r_1, paco5_2_1 gf_0 gf_1 (upaco5_2_0 gf_0 gf_1 r_0 r_1) (upaco5_2_1 gf_0 gf_1 r_0 r_1) <5= paco5_2_1 gf_0 gf_1 r_0 r_1.