Instance paco5_2_0_inst  T0 T1 T2 T3 T4 (gf_0 gf_1 : rel5 T0 T1 T2 T3 T4->_) r_0 r_1 x0 x1 x2 x3 x4 : paco_class (paco5_2_0 gf_0 gf_1 r_0 r_1 x0 x1 x2 x3 x4) :=
{ pacoacc    := paco5_2_0_acc gf_0 gf_1;
  pacomult   := paco5_2_0_mult gf_0 gf_1;
  pacofold   := paco5_2_0_fold gf_0 gf_1;
  pacounfold := paco5_2_0_unfold gf_0 gf_1 }.Instance paco5_2_1_inst  T0 T1 T2 T3 T4 (gf_0 gf_1 : rel5 T0 T1 T2 T3 T4->_) r_0 r_1 x0 x1 x2 x3 x4 : paco_class (paco5_2_1 gf_0 gf_1 r_0 r_1 x0 x1 x2 x3 x4) :=
{ pacoacc    := paco5_2_1_acc gf_0 gf_1;
  pacomult   := paco5_2_1_mult gf_0 gf_1;
  pacofold   := paco5_2_1_fold gf_0 gf_1;
  pacounfold := paco5_2_1_unfold gf_0 gf_1 }.Definition monotone5_3 T0 T1 T2 T3 T4 (gf: rel5 T0 T1 T2 T3 T4 -> 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_2 r'_0 r'_1 r'_2 (IN: gf r_0 r_1 r_2 x0 x1 x2 x3 x4) (LE_0: r_0 <5= r'_0)(LE_1: r_1 <5= r'_1)(LE_2: r_2 <5= r'_2), gf r'_0 r'_1 r'_2 x0 x1 x2 x3 x4.

(* Specifications: *)
Theorem paco5_3_0_acc: forall l r_0 r_1 r_2 (OBG: forall rr (INC: r_0 <5= rr) (CIH: l <_paco_5= rr), l <_paco_5= paco5_3_0 gf_0 gf_1 gf_2 rr r_1 r_2), l <5= paco5_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco5_3_1_acc: forall l r_0 r_1 r_2 (OBG: forall rr (INC: r_1 <5= rr) (CIH: l <_paco_5= rr), l <_paco_5= paco5_3_1 gf_0 gf_1 gf_2 r_0 rr r_2), l <5= paco5_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco5_3_2_acc: forall l r_0 r_1 r_2 (OBG: forall rr (INC: r_2 <5= rr) (CIH: l <_paco_5= rr), l <_paco_5= paco5_3_2 gf_0 gf_1 gf_2 r_0 r_1 rr), l <5= paco5_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco5_3_0_mon: monotone5_3 (paco5_3_0 gf_0 gf_1 gf_2).
Theorem paco5_3_1_mon: monotone5_3 (paco5_3_1 gf_0 gf_1 gf_2).
Theorem paco5_3_2_mon: monotone5_3 (paco5_3_2 gf_0 gf_1 gf_2).
Theorem paco5_3_0_mult_strong: forall r_0 r_1 r_2, paco5_3_0 gf_0 gf_1 gf_2 (upaco5_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco5_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco5_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <5= paco5_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco5_3_1_mult_strong: forall r_0 r_1 r_2, paco5_3_1 gf_0 gf_1 gf_2 (upaco5_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco5_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco5_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <5= paco5_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco5_3_2_mult_strong: forall r_0 r_1 r_2, paco5_3_2 gf_0 gf_1 gf_2 (upaco5_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco5_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco5_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <5= paco5_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.