Section PACO14.
Variable T0 : Type.
Variable T1 : forall (x0: @T0), Type.
Variable T2 : forall (x0: @T0) (x1: @T1 x0), Type.
Variable T3 : forall (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1), Type.
Variable T4 : forall (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2), Type.
Variable T5 : forall (x0: @T0) (x1: @T1 x0) (x2: @T2 x0 x1) (x3: @T3 x0 x1 x2) (x4: @T4 x0 x1 x2 x3), Type.
Variable T6 : forall (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 : forall (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 : forall (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 : forall (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 : forall (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 : forall (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 : forall (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 : forall (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.
(** ** Signatures *)
Record sig14T  :=
exist14T {
proj14T0: @T0;
proj14T1: @T1 proj14T0;
proj14T2: @T2 proj14T0 proj14T1;
proj14T3: @T3 proj14T0 proj14T1 proj14T2;
proj14T4: @T4 proj14T0 proj14T1 proj14T2 proj14T3;
proj14T5: @T5 proj14T0 proj14T1 proj14T2 proj14T3 proj14T4;
proj14T6: @T6 proj14T0 proj14T1 proj14T2 proj14T3 proj14T4 proj14T5;
proj14T7: @T7 proj14T0 proj14T1 proj14T2 proj14T3 proj14T4 proj14T5 proj14T6;
proj14T8: @T8 proj14T0 proj14T1 proj14T2 proj14T3 proj14T4 proj14T5 proj14T6 proj14T7;
proj14T9: @T9 proj14T0 proj14T1 proj14T2 proj14T3 proj14T4 proj14T5 proj14T6 proj14T7 proj14T8;
proj14T10: @T10 proj14T0 proj14T1 proj14T2 proj14T3 proj14T4 proj14T5 proj14T6 proj14T7 proj14T8 proj14T9;
proj14T11: @T11 proj14T0 proj14T1 proj14T2 proj14T3 proj14T4 proj14T5 proj14T6 proj14T7 proj14T8 proj14T9 proj14T10;
proj14T12: @T12 proj14T0 proj14T1 proj14T2 proj14T3 proj14T4 proj14T5 proj14T6 proj14T7 proj14T8 proj14T9 proj14T10 proj14T11;
proj14T13: @T13 proj14T0 proj14T1 proj14T2 proj14T3 proj14T4 proj14T5 proj14T6 proj14T7 proj14T8 proj14T9 proj14T10 proj14T11 proj14T12;
}.
Definition uncurry14  (R: rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13): rel1 sig14T :=
fun x => R (proj14T0 x) (proj14T1 x) (proj14T2 x) (proj14T3 x) (proj14T4 x) (proj14T5 x) (proj14T6 x) (proj14T7 x) (proj14T8 x) (proj14T9 x) (proj14T10 x) (proj14T11 x) (proj14T12 x) (proj14T13 x).
Definition curry14  (R: rel1 sig14T): rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 :=
fun x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 => R (@exist14T x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13).
(** ** Predicates of Arity 14 *)
Definition paco14(gf : rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 -> rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13)(r: rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13) : rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 :=
curry14 (paco (fun R0 => uncurry14 (gf (curry14 R0))) (uncurry14 r)).
Definition upaco14(gf : rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 -> rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13)(r: rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13) := paco14 gf r \14/ r.
Arguments paco14 : clear implicits.
Arguments upaco14 : clear implicits.
Hint Unfold upaco14 : core.
Definition monotone14 (gf: rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 -> rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13) :=
forall x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r r' (IN: gf r x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) (LE: r <14= r'), gf r' x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13.
Definition _monotone14 (gf: rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 -> rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13) :=
forall r r'(LE: r <14= r'), gf r <14== gf r'.

Lemma monotone14_union (gf gf': rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 -> rel14 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13)
(MON1: monotone14 gf)
(MON2: monotone14 gf'):
monotone14 (gf \15/ gf').