Instance paco2_2_0_inst  T0 T1 (gf_0 gf_1 : rel2 T0 T1->_) r_0 r_1 x0 x1 : paco_class (paco2_2_0 gf_0 gf_1 r_0 r_1 x0 x1) :=
{ pacoacc    := paco2_2_0_acc gf_0 gf_1;
  pacomult   := paco2_2_0_mult gf_0 gf_1;
  pacofold   := paco2_2_0_fold gf_0 gf_1;
  pacounfold := paco2_2_0_unfold gf_0 gf_1 }.Instance paco2_2_1_inst  T0 T1 (gf_0 gf_1 : rel2 T0 T1->_) r_0 r_1 x0 x1 : paco_class (paco2_2_1 gf_0 gf_1 r_0 r_1 x0 x1) :=
{ pacoacc    := paco2_2_1_acc gf_0 gf_1;
  pacomult   := paco2_2_1_mult gf_0 gf_1;
  pacofold   := paco2_2_1_fold gf_0 gf_1;
  pacounfold := paco2_2_1_unfold gf_0 gf_1 }.Definition monotone2_3 T0 T1 (gf: rel2 T0 T1 -> rel2 T0 T1 -> rel2 T0 T1 -> rel2 T0 T1) :=
  forall x0 x1 r_0 r_1 r_2 r'_0 r'_1 r'_2 (IN: gf r_0 r_1 r_2 x0 x1) (LE_0: r_0 <2= r'_0)(LE_1: r_1 <2= r'_1)(LE_2: r_2 <2= r'_2), gf r'_0 r'_1 r'_2 x0 x1.

(* Specifications: *)
Theorem paco2_3_0_acc: forall l r_0 r_1 r_2 (OBG: forall rr (INC: r_0 <2= rr) (CIH: l <_paco_2= rr), l <_paco_2= paco2_3_0 gf_0 gf_1 gf_2 rr r_1 r_2), l <2= paco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco2_3_1_acc: forall l r_0 r_1 r_2 (OBG: forall rr (INC: r_1 <2= rr) (CIH: l <_paco_2= rr), l <_paco_2= paco2_3_1 gf_0 gf_1 gf_2 r_0 rr r_2), l <2= paco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco2_3_2_acc: forall l r_0 r_1 r_2 (OBG: forall rr (INC: r_2 <2= rr) (CIH: l <_paco_2= rr), l <_paco_2= paco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 rr), l <2= paco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco2_3_0_mon: monotone2_3 (paco2_3_0 gf_0 gf_1 gf_2).
Theorem paco2_3_1_mon: monotone2_3 (paco2_3_1 gf_0 gf_1 gf_2).
Theorem paco2_3_2_mon: monotone2_3 (paco2_3_2 gf_0 gf_1 gf_2).
Theorem paco2_3_0_mult_strong: forall r_0 r_1 r_2, paco2_3_0 gf_0 gf_1 gf_2 (upaco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <2= paco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco2_3_1_mult_strong: forall r_0 r_1 r_2, paco2_3_1 gf_0 gf_1 gf_2 (upaco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <2= paco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco2_3_2_mult_strong: forall r_0 r_1 r_2, paco2_3_2 gf_0 gf_1 gf_2 (upaco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <2= paco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.