Instance paco3_2_0_inst  T0 T1 T2 (gf_0 gf_1 : rel3 T0 T1 T2->_) r_0 r_1 x0 x1 x2 : paco_class (paco3_2_0 gf_0 gf_1 r_0 r_1 x0 x1 x2) :=
{ pacoacc    := paco3_2_0_acc gf_0 gf_1;
  pacomult   := paco3_2_0_mult gf_0 gf_1;
  pacofold   := paco3_2_0_fold gf_0 gf_1;
  pacounfold := paco3_2_0_unfold gf_0 gf_1 }.Instance paco3_2_1_inst  T0 T1 T2 (gf_0 gf_1 : rel3 T0 T1 T2->_) r_0 r_1 x0 x1 x2 : paco_class (paco3_2_1 gf_0 gf_1 r_0 r_1 x0 x1 x2) :=
{ pacoacc    := paco3_2_1_acc gf_0 gf_1;
  pacomult   := paco3_2_1_mult gf_0 gf_1;
  pacofold   := paco3_2_1_fold gf_0 gf_1;
  pacounfold := paco3_2_1_unfold gf_0 gf_1 }.Definition monotone3_3 T0 T1 T2 (gf: rel3 T0 T1 T2 -> rel3 T0 T1 T2 -> rel3 T0 T1 T2 -> rel3 T0 T1 T2) :=
  forall x0 x1 x2 r_0 r_1 r_2 r'_0 r'_1 r'_2 (IN: gf r_0 r_1 r_2 x0 x1 x2) (LE_0: r_0 <3= r'_0)(LE_1: r_1 <3= r'_1)(LE_2: r_2 <3= r'_2), gf r'_0 r'_1 r'_2 x0 x1 x2.

(* Specifications: *)
Theorem paco3_3_0_acc: forall l r_0 r_1 r_2 (OBG: forall rr (INC: r_0 <3= rr) (CIH: l <_paco_3= rr), l <_paco_3= paco3_3_0 gf_0 gf_1 gf_2 rr r_1 r_2), l <3= paco3_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco3_3_1_acc: forall l r_0 r_1 r_2 (OBG: forall rr (INC: r_1 <3= rr) (CIH: l <_paco_3= rr), l <_paco_3= paco3_3_1 gf_0 gf_1 gf_2 r_0 rr r_2), l <3= paco3_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco3_3_2_acc: forall l r_0 r_1 r_2 (OBG: forall rr (INC: r_2 <3= rr) (CIH: l <_paco_3= rr), l <_paco_3= paco3_3_2 gf_0 gf_1 gf_2 r_0 r_1 rr), l <3= paco3_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco3_3_0_mon: monotone3_3 (paco3_3_0 gf_0 gf_1 gf_2).
Theorem paco3_3_1_mon: monotone3_3 (paco3_3_1 gf_0 gf_1 gf_2).
Theorem paco3_3_2_mon: monotone3_3 (paco3_3_2 gf_0 gf_1 gf_2).
Theorem paco3_3_0_mult_strong: forall r_0 r_1 r_2, paco3_3_0 gf_0 gf_1 gf_2 (upaco3_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco3_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco3_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <3= paco3_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco3_3_1_mult_strong: forall r_0 r_1 r_2, paco3_3_1 gf_0 gf_1 gf_2 (upaco3_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco3_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco3_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <3= paco3_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco3_3_2_mult_strong: forall r_0 r_1 r_2, paco3_3_2 gf_0 gf_1 gf_2 (upaco3_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco3_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco3_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <3= paco3_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.