Lvc.paco.paco14

Require Export paconotation pacotac pacodef pacotacuser.
Set Implicit Arguments.

Predicates of Arity 14

1 Mutual Coinduction

Section Arg14_1.

Definition monotone14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 (gf: rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13) :=
   x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r (IN: gf r x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) (LE: r <14= ), gf x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13.

Variable T0 : Type.
Variable T1 : (x0: @T0), Type.
Variable T2 : (x0: @T0) (x1: @T1 x0), Type.
Variable T3 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1), Type.
Variable T4 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2), Type.
Variable T5 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3), Type.
Variable T6 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4), Type.
Variable T7 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5), Type.
Variable T8 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6), Type.
Variable T9 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7), Type.
Variable T10 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7) (x9: @T9 x0 x1 x2 x3 x4 x5 x6 x7 x8), Type.
Variable T11 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7) (x9: @T9 x0 x1 x2 x3 x4 x5 x6 x7 x8) (x10: @T10 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9), Type.
Variable T12 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7) (x9: @T9 x0 x1 x2 x3 x4 x5 x6 x7 x8) (x10: @T10 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9) (x11: @T11 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10), Type.
Variable T13 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7) (x9: @T9 x0 x1 x2 x3 x4 x5 x6 x7 x8) (x10: @T10 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9) (x11: @T11 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10) (x12: @T12 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11), Type.
Variable gf : rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13.
Implicit Arguments gf [].

Theorem paco14_acc:
  l r (OBG: rr (INC: r <14= rr) (CIH: l <_paco_14= rr), l <_paco_14= paco14 gf rr),
  l <14= paco14 gf r.
Proof.
  intros; assert (SIM: paco14 gf (r \14/ l) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) by eauto.
  clear PR; repeat (try left; do 15 paco_revert; paco_cofix_auto).
Qed.

Theorem paco14_mon: monotone14 (paco14 gf).
Proof. paco_cofix_auto; repeat (left; do 15 paco_revert; paco_cofix_auto). Qed.

Theorem paco14_mult_strong: r,
  paco14 gf (paco14 gf r \14/ r) <14= paco14 gf r.
Proof. paco_cofix_auto; repeat (left; do 15 paco_revert; paco_cofix_auto). Qed.

Corollary paco14_mult: r,
  paco14 gf (paco14 gf r) <14= paco14 gf r.
Proof. intros; eapply paco14_mult_strong, paco14_mon; eauto. Qed.

Theorem paco14_fold: r,
  gf (paco14 gf r \14/ r) <14= paco14 gf r.
Proof. intros; econstructor; [ |eauto]; eauto. Qed.

Theorem paco14_unfold: (MON: monotone14 gf) r,
  paco14 gf r <14= gf (paco14 gf r \14/ r).
Proof. unfold monotone14; intros; destruct PR; eauto. Qed.

End Arg14_1.

Hint Unfold monotone14.
Hint Resolve paco14_fold.

Implicit Arguments paco14_acc [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_mon [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_mult_strong [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_mult [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_fold [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_unfold [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].

Instance paco14_inst T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 (gf : rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13_) r x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : paco_class (paco14 gf r x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) :=
{ pacoacc := paco14_acc gf;
  pacomult := paco14_mult gf;
  pacofold := paco14_fold gf;
  pacounfold := paco14_unfold gf }.

2 Mutual Coinduction

Section Arg14_2.

Definition monotone14_2 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 (gf: rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13) :=
   x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r_0 r_1 r´_0 r´_1 (IN: gf r_0 r_1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) (LE_0: r_0 <14= r´_0)(LE_1: r_1 <14= r´_1), gf r´_0 r´_1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13.

Variable T0 : Type.
Variable T1 : (x0: @T0), Type.
Variable T2 : (x0: @T0) (x1: @T1 x0), Type.
Variable T3 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1), Type.
Variable T4 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2), Type.
Variable T5 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3), Type.
Variable T6 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4), Type.
Variable T7 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5), Type.
Variable T8 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6), Type.
Variable T9 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7), Type.
Variable T10 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7) (x9: @T9 x0 x1 x2 x3 x4 x5 x6 x7 x8), Type.
Variable T11 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7) (x9: @T9 x0 x1 x2 x3 x4 x5 x6 x7 x8) (x10: @T10 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9), Type.
Variable T12 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7) (x9: @T9 x0 x1 x2 x3 x4 x5 x6 x7 x8) (x10: @T10 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9) (x11: @T11 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10), Type.
Variable T13 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7) (x9: @T9 x0 x1 x2 x3 x4 x5 x6 x7 x8) (x10: @T10 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9) (x11: @T11 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10) (x12: @T12 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11), Type.
Variable gf_0 gf_1 : rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13.
Implicit Arguments gf_0 [].
Implicit Arguments gf_1 [].

Theorem paco14_2_0_acc:
  l r_0 r_1 (OBG: rr (INC: r_0 <14= rr) (CIH: l <_paco_14= rr), l <_paco_14= paco14_2_0 gf_0 gf_1 rr r_1),
  l <14= paco14_2_0 gf_0 gf_1 r_0 r_1.
Proof.
  intros; assert (SIM: paco14_2_0 gf_0 gf_1 (r_0 \14/ l) r_1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) by eauto.
  clear PR; repeat (try left; do 15 paco_revert; paco_cofix_auto).
Qed.

Theorem paco14_2_1_acc:
  l r_0 r_1 (OBG: rr (INC: r_1 <14= rr) (CIH: l <_paco_14= rr), l <_paco_14= paco14_2_1 gf_0 gf_1 r_0 rr),
  l <14= paco14_2_1 gf_0 gf_1 r_0 r_1.
Proof.
  intros; assert (SIM: paco14_2_1 gf_0 gf_1 r_0 (r_1 \14/ l) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) by eauto.
  clear PR; repeat (try left; do 15 paco_revert; paco_cofix_auto).
Qed.

Theorem paco14_2_0_mon: monotone14_2 (paco14_2_0 gf_0 gf_1).
Proof. paco_cofix_auto; repeat (left; do 15 paco_revert; paco_cofix_auto). Qed.

Theorem paco14_2_1_mon: monotone14_2 (paco14_2_1 gf_0 gf_1).
Proof. paco_cofix_auto; repeat (left; do 15 paco_revert; paco_cofix_auto). Qed.

Theorem paco14_2_0_mult_strong: r_0 r_1,
  paco14_2_0 gf_0 gf_1 (paco14_2_0 gf_0 gf_1 r_0 r_1 \14/ r_0) (paco14_2_1 gf_0 gf_1 r_0 r_1 \14/ r_1) <14= paco14_2_0 gf_0 gf_1 r_0 r_1.
Proof. paco_cofix_auto; repeat (left; do 15 paco_revert; paco_cofix_auto). Qed.

Theorem paco14_2_1_mult_strong: r_0 r_1,
  paco14_2_1 gf_0 gf_1 (paco14_2_0 gf_0 gf_1 r_0 r_1 \14/ r_0) (paco14_2_1 gf_0 gf_1 r_0 r_1 \14/ r_1) <14= paco14_2_1 gf_0 gf_1 r_0 r_1.
Proof. paco_cofix_auto; repeat (left; do 15 paco_revert; paco_cofix_auto). Qed.

Corollary paco14_2_0_mult: r_0 r_1,
  paco14_2_0 gf_0 gf_1 (paco14_2_0 gf_0 gf_1 r_0 r_1) (paco14_2_1 gf_0 gf_1 r_0 r_1) <14= paco14_2_0 gf_0 gf_1 r_0 r_1.
Proof. intros; eapply paco14_2_0_mult_strong, paco14_2_0_mon; eauto. Qed.

Corollary paco14_2_1_mult: r_0 r_1,
  paco14_2_1 gf_0 gf_1 (paco14_2_0 gf_0 gf_1 r_0 r_1) (paco14_2_1 gf_0 gf_1 r_0 r_1) <14= paco14_2_1 gf_0 gf_1 r_0 r_1.
Proof. intros; eapply paco14_2_1_mult_strong, paco14_2_1_mon; eauto. Qed.

Theorem paco14_2_0_fold: r_0 r_1,
  gf_0 (paco14_2_0 gf_0 gf_1 r_0 r_1 \14/ r_0) (paco14_2_1 gf_0 gf_1 r_0 r_1 \14/ r_1) <14= paco14_2_0 gf_0 gf_1 r_0 r_1.
Proof. intros; econstructor; [ | |eauto]; eauto. Qed.

Theorem paco14_2_1_fold: r_0 r_1,
  gf_1 (paco14_2_0 gf_0 gf_1 r_0 r_1 \14/ r_0) (paco14_2_1 gf_0 gf_1 r_0 r_1 \14/ r_1) <14= paco14_2_1 gf_0 gf_1 r_0 r_1.
Proof. intros; econstructor; [ | |eauto]; eauto. Qed.

Theorem paco14_2_0_unfold: (MON: monotone14_2 gf_0) (MON: monotone14_2 gf_1) r_0 r_1,
  paco14_2_0 gf_0 gf_1 r_0 r_1 <14= gf_0 (paco14_2_0 gf_0 gf_1 r_0 r_1 \14/ r_0) (paco14_2_1 gf_0 gf_1 r_0 r_1 \14/ r_1).
Proof. unfold monotone14_2; intros; destruct PR; eauto. Qed.

Theorem paco14_2_1_unfold: (MON: monotone14_2 gf_0) (MON: monotone14_2 gf_1) r_0 r_1,
  paco14_2_1 gf_0 gf_1 r_0 r_1 <14= gf_1 (paco14_2_0 gf_0 gf_1 r_0 r_1 \14/ r_0) (paco14_2_1 gf_0 gf_1 r_0 r_1 \14/ r_1).
Proof. unfold monotone14_2; intros; destruct PR; eauto. Qed.

End Arg14_2.

Hint Unfold monotone14_2.
Hint Resolve paco14_2_0_fold.
Hint Resolve paco14_2_1_fold.

Implicit Arguments paco14_2_0_acc [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_2_1_acc [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_2_0_mon [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_2_1_mon [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_2_0_mult_strong [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_2_1_mult_strong [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_2_0_mult [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_2_1_mult [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_2_0_fold [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_2_1_fold [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_2_0_unfold [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_2_1_unfold [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].

Instance paco14_2_0_inst T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 (gf_0 gf_1 : rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13_) r_0 r_1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : paco_class (paco14_2_0 gf_0 gf_1 r_0 r_1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) :=
{ pacoacc := paco14_2_0_acc gf_0 gf_1;
  pacomult := paco14_2_0_mult gf_0 gf_1;
  pacofold := paco14_2_0_fold gf_0 gf_1;
  pacounfold := paco14_2_0_unfold gf_0 gf_1 }.

Instance paco14_2_1_inst T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 (gf_0 gf_1 : rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13_) r_0 r_1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : paco_class (paco14_2_1 gf_0 gf_1 r_0 r_1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) :=
{ pacoacc := paco14_2_1_acc gf_0 gf_1;
  pacomult := paco14_2_1_mult gf_0 gf_1;
  pacofold := paco14_2_1_fold gf_0 gf_1;
  pacounfold := paco14_2_1_unfold gf_0 gf_1 }.

3 Mutual Coinduction

Section Arg14_3.

Definition monotone14_3 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 (gf: rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13) :=
   x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 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 x5 x6 x7 x8 x9 x10 x11 x12 x13) (LE_0: r_0 <14= r´_0)(LE_1: r_1 <14= r´_1)(LE_2: r_2 <14= r´_2), gf r´_0 r´_1 r´_2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13.

Variable T0 : Type.
Variable T1 : (x0: @T0), Type.
Variable T2 : (x0: @T0) (x1: @T1 x0), Type.
Variable T3 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1), Type.
Variable T4 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2), Type.
Variable T5 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3), Type.
Variable T6 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4), Type.
Variable T7 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5), Type.
Variable T8 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6), Type.
Variable T9 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7), Type.
Variable T10 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7) (x9: @T9 x0 x1 x2 x3 x4 x5 x6 x7 x8), Type.
Variable T11 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7) (x9: @T9 x0 x1 x2 x3 x4 x5 x6 x7 x8) (x10: @T10 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9), Type.
Variable T12 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7) (x9: @T9 x0 x1 x2 x3 x4 x5 x6 x7 x8) (x10: @T10 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9) (x11: @T11 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10), Type.
Variable T13 : (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3) (x5: @T5 x0 x1 x2 x3 x4) (x6: @T6 x0 x1 x2 x3 x4 x5) (x7: @T7 x0 x1 x2 x3 x4 x5 x6) (x8: @T8 x0 x1 x2 x3 x4 x5 x6 x7) (x9: @T9 x0 x1 x2 x3 x4 x5 x6 x7 x8) (x10: @T10 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9) (x11: @T11 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10) (x12: @T12 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11), Type.
Variable gf_0 gf_1 gf_2 : rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13.
Implicit Arguments gf_0 [].
Implicit Arguments gf_1 [].
Implicit Arguments gf_2 [].

Theorem paco14_3_0_acc:
  l r_0 r_1 r_2 (OBG: rr (INC: r_0 <14= rr) (CIH: l <_paco_14= rr), l <_paco_14= paco14_3_0 gf_0 gf_1 gf_2 rr r_1 r_2),
  l <14= paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Proof.
  intros; assert (SIM: paco14_3_0 gf_0 gf_1 gf_2 (r_0 \14/ l) r_1 r_2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) by eauto.
  clear PR; repeat (try left; do 15 paco_revert; paco_cofix_auto).
Qed.

Theorem paco14_3_1_acc:
  l r_0 r_1 r_2 (OBG: rr (INC: r_1 <14= rr) (CIH: l <_paco_14= rr), l <_paco_14= paco14_3_1 gf_0 gf_1 gf_2 r_0 rr r_2),
  l <14= paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Proof.
  intros; assert (SIM: paco14_3_1 gf_0 gf_1 gf_2 r_0 (r_1 \14/ l) r_2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) by eauto.
  clear PR; repeat (try left; do 15 paco_revert; paco_cofix_auto).
Qed.

Theorem paco14_3_2_acc:
  l r_0 r_1 r_2 (OBG: rr (INC: r_2 <14= rr) (CIH: l <_paco_14= rr), l <_paco_14= paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 rr),
  l <14= paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Proof.
  intros; assert (SIM: paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 (r_2 \14/ l) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) by eauto.
  clear PR; repeat (try left; do 15 paco_revert; paco_cofix_auto).
Qed.

Theorem paco14_3_0_mon: monotone14_3 (paco14_3_0 gf_0 gf_1 gf_2).
Proof. paco_cofix_auto; repeat (left; do 15 paco_revert; paco_cofix_auto). Qed.

Theorem paco14_3_1_mon: monotone14_3 (paco14_3_1 gf_0 gf_1 gf_2).
Proof. paco_cofix_auto; repeat (left; do 15 paco_revert; paco_cofix_auto). Qed.

Theorem paco14_3_2_mon: monotone14_3 (paco14_3_2 gf_0 gf_1 gf_2).
Proof. paco_cofix_auto; repeat (left; do 15 paco_revert; paco_cofix_auto). Qed.

Theorem paco14_3_0_mult_strong: r_0 r_1 r_2,
  paco14_3_0 gf_0 gf_1 gf_2 (paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_0) (paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_1) (paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_2) <14= paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Proof. paco_cofix_auto; repeat (left; do 15 paco_revert; paco_cofix_auto). Qed.

Theorem paco14_3_1_mult_strong: r_0 r_1 r_2,
  paco14_3_1 gf_0 gf_1 gf_2 (paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_0) (paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_1) (paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_2) <14= paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Proof. paco_cofix_auto; repeat (left; do 15 paco_revert; paco_cofix_auto). Qed.

Theorem paco14_3_2_mult_strong: r_0 r_1 r_2,
  paco14_3_2 gf_0 gf_1 gf_2 (paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_0) (paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_1) (paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_2) <14= paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Proof. paco_cofix_auto; repeat (left; do 15 paco_revert; paco_cofix_auto). Qed.

Corollary paco14_3_0_mult: r_0 r_1 r_2,
  paco14_3_0 gf_0 gf_1 gf_2 (paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <14= paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Proof. intros; eapply paco14_3_0_mult_strong, paco14_3_0_mon; eauto. Qed.

Corollary paco14_3_1_mult: r_0 r_1 r_2,
  paco14_3_1 gf_0 gf_1 gf_2 (paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <14= paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Proof. intros; eapply paco14_3_1_mult_strong, paco14_3_1_mon; eauto. Qed.

Corollary paco14_3_2_mult: r_0 r_1 r_2,
  paco14_3_2 gf_0 gf_1 gf_2 (paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <14= paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Proof. intros; eapply paco14_3_2_mult_strong, paco14_3_2_mon; eauto. Qed.

Theorem paco14_3_0_fold: r_0 r_1 r_2,
  gf_0 (paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_0) (paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_1) (paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_2) <14= paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Proof. intros; econstructor; [ | | |eauto]; eauto. Qed.

Theorem paco14_3_1_fold: r_0 r_1 r_2,
  gf_1 (paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_0) (paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_1) (paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_2) <14= paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Proof. intros; econstructor; [ | | |eauto]; eauto. Qed.

Theorem paco14_3_2_fold: r_0 r_1 r_2,
  gf_2 (paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_0) (paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_1) (paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_2) <14= paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Proof. intros; econstructor; [ | | |eauto]; eauto. Qed.

Theorem paco14_3_0_unfold: (MON: monotone14_3 gf_0) (MON: monotone14_3 gf_1) (MON: monotone14_3 gf_2) r_0 r_1 r_2,
  paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2 <14= gf_0 (paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_0) (paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_1) (paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_2).
Proof. unfold monotone14_3; intros; destruct PR; eauto. Qed.

Theorem paco14_3_1_unfold: (MON: monotone14_3 gf_0) (MON: monotone14_3 gf_1) (MON: monotone14_3 gf_2) r_0 r_1 r_2,
  paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2 <14= gf_1 (paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_0) (paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_1) (paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_2).
Proof. unfold monotone14_3; intros; destruct PR; eauto. Qed.

Theorem paco14_3_2_unfold: (MON: monotone14_3 gf_0) (MON: monotone14_3 gf_1) (MON: monotone14_3 gf_2) r_0 r_1 r_2,
  paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2 <14= gf_2 (paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_0) (paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_1) (paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2 \14/ r_2).
Proof. unfold monotone14_3; intros; destruct PR; eauto. Qed.

End Arg14_3.

Hint Unfold monotone14_3.
Hint Resolve paco14_3_0_fold.
Hint Resolve paco14_3_1_fold.
Hint Resolve paco14_3_2_fold.

Implicit Arguments paco14_3_0_acc [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_1_acc [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_2_acc [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_0_mon [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_1_mon [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_2_mon [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_0_mult_strong [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_1_mult_strong [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_2_mult_strong [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_0_mult [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_1_mult [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_2_mult [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_0_fold [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_1_fold [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_2_fold [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_0_unfold [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_1_unfold [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].
Implicit Arguments paco14_3_2_unfold [ T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 ].

Instance paco14_3_0_inst T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 (gf_0 gf_1 gf_2 : rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13_) r_0 r_1 r_2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : paco_class (paco14_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) :=
{ pacoacc := paco14_3_0_acc gf_0 gf_1 gf_2;
  pacomult := paco14_3_0_mult gf_0 gf_1 gf_2;
  pacofold := paco14_3_0_fold gf_0 gf_1 gf_2;
  pacounfold := paco14_3_0_unfold gf_0 gf_1 gf_2 }.

Instance paco14_3_1_inst T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 (gf_0 gf_1 gf_2 : rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13_) r_0 r_1 r_2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : paco_class (paco14_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) :=
{ pacoacc := paco14_3_1_acc gf_0 gf_1 gf_2;
  pacomult := paco14_3_1_mult gf_0 gf_1 gf_2;
  pacofold := paco14_3_1_fold gf_0 gf_1 gf_2;
  pacounfold := paco14_3_1_unfold gf_0 gf_1 gf_2 }.

Instance paco14_3_2_inst T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 (gf_0 gf_1 gf_2 : rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13_) r_0 r_1 r_2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : paco_class (paco14_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) :=
{ pacoacc := paco14_3_2_acc gf_0 gf_1 gf_2;
  pacomult := paco14_3_2_mult gf_0 gf_1 gf_2;
  pacofold := paco14_3_2_fold gf_0 gf_1 gf_2;
  pacounfold := paco14_3_2_unfold gf_0 gf_1 gf_2 }.