Instance paco4_2_0_inst  T0 T1 T2 T3 (gf_0 gf_1 : rel4 T0 T1 T2 T3->_) r_0 r_1 x0 x1 x2 x3 : paco_class (paco4_2_0 gf_0 gf_1 r_0 r_1 x0 x1 x2 x3) :=
{ pacoacc    := paco4_2_0_acc gf_0 gf_1;
  pacomult   := paco4_2_0_mult gf_0 gf_1;
  pacofold   := paco4_2_0_fold gf_0 gf_1;
  pacounfold := paco4_2_0_unfold gf_0 gf_1 }.Instance paco4_2_1_inst  T0 T1 T2 T3 (gf_0 gf_1 : rel4 T0 T1 T2 T3->_) r_0 r_1 x0 x1 x2 x3 : paco_class (paco4_2_1 gf_0 gf_1 r_0 r_1 x0 x1 x2 x3) :=
{ pacoacc    := paco4_2_1_acc gf_0 gf_1;
  pacomult   := paco4_2_1_mult gf_0 gf_1;
  pacofold   := paco4_2_1_fold gf_0 gf_1;
  pacounfold := paco4_2_1_unfold gf_0 gf_1 }.Definition monotone4_3 T0 T1 T2 T3 (gf: rel4 T0 T1 T2 T3 -> rel4 T0 T1 T2 T3 -> rel4 T0 T1 T2 T3 -> rel4 T0 T1 T2 T3) :=
  forall x0 x1 x2 x3 r_0 r_1 r_2 r'_0 r'_1 r'_2 (IN: gf r_0 r_1 r_2 x0 x1 x2 x3) (LE_0: r_0 <4= r'_0)(LE_1: r_1 <4= r'_1)(LE_2: r_2 <4= r'_2), gf r'_0 r'_1 r'_2 x0 x1 x2 x3.

(* Specifications: *)
Theorem paco4_3_0_acc: forall l r_0 r_1 r_2 (OBG: forall rr (INC: r_0 <4= rr) (CIH: l <_paco_4= rr), l <_paco_4= paco4_3_0 gf_0 gf_1 gf_2 rr r_1 r_2), l <4= paco4_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco4_3_1_acc: forall l r_0 r_1 r_2 (OBG: forall rr (INC: r_1 <4= rr) (CIH: l <_paco_4= rr), l <_paco_4= paco4_3_1 gf_0 gf_1 gf_2 r_0 rr r_2), l <4= paco4_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco4_3_2_acc: forall l r_0 r_1 r_2 (OBG: forall rr (INC: r_2 <4= rr) (CIH: l <_paco_4= rr), l <_paco_4= paco4_3_2 gf_0 gf_1 gf_2 r_0 r_1 rr), l <4= paco4_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco4_3_0_mon: monotone4_3 (paco4_3_0 gf_0 gf_1 gf_2).
Theorem paco4_3_1_mon: monotone4_3 (paco4_3_1 gf_0 gf_1 gf_2).
Theorem paco4_3_2_mon: monotone4_3 (paco4_3_2 gf_0 gf_1 gf_2).
Theorem paco4_3_0_mult_strong: forall r_0 r_1 r_2, paco4_3_0 gf_0 gf_1 gf_2 (upaco4_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco4_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco4_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <4= paco4_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco4_3_1_mult_strong: forall r_0 r_1 r_2, paco4_3_1 gf_0 gf_1 gf_2 (upaco4_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco4_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco4_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <4= paco4_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco4_3_2_mult_strong: forall r_0 r_1 r_2, paco4_3_2 gf_0 gf_1 gf_2 (upaco4_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco4_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco4_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <4= paco4_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.