Section PACO10.
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.
(** ** Signatures *)
Record sig10T  :=
exist10T {
proj10T0: @T0;
proj10T1: @T1 proj10T0;
proj10T2: @T2 proj10T0 proj10T1;
proj10T3: @T3 proj10T0 proj10T1 proj10T2;
proj10T4: @T4 proj10T0 proj10T1 proj10T2 proj10T3;
proj10T5: @T5 proj10T0 proj10T1 proj10T2 proj10T3 proj10T4;
proj10T6: @T6 proj10T0 proj10T1 proj10T2 proj10T3 proj10T4 proj10T5;
proj10T7: @T7 proj10T0 proj10T1 proj10T2 proj10T3 proj10T4 proj10T5 proj10T6;
proj10T8: @T8 proj10T0 proj10T1 proj10T2 proj10T3 proj10T4 proj10T5 proj10T6 proj10T7;
proj10T9: @T9 proj10T0 proj10T1 proj10T2 proj10T3 proj10T4 proj10T5 proj10T6 proj10T7 proj10T8;
}.
Definition uncurry10  (R: rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9): rel1 sig10T :=
fun x => R (proj10T0 x) (proj10T1 x) (proj10T2 x) (proj10T3 x) (proj10T4 x) (proj10T5 x) (proj10T6 x) (proj10T7 x) (proj10T8 x) (proj10T9 x).
Definition curry10  (R: rel1 sig10T): rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 :=
fun x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 => R (@exist10T x0 x1 x2 x3 x4 x5 x6 x7 x8 x9).
(** ** Predicates of Arity 10 *)
Definition paco10(gf : rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 -> rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9)(r: rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9) : rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 :=
curry10 (paco (fun R0 => uncurry10 (gf (curry10 R0))) (uncurry10 r)).
Definition upaco10(gf : rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 -> rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9)(r: rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9) := paco10 gf r \10/ r.
Arguments paco10 : clear implicits.
Arguments upaco10 : clear implicits.
Hint Unfold upaco10 : core.
Definition monotone10 (gf: rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 -> rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9) :=
forall x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r r' (IN: gf r x0 x1 x2 x3 x4 x5 x6 x7 x8 x9) (LE: r <10= r'), gf r' x0 x1 x2 x3 x4 x5 x6 x7 x8 x9.
Definition _monotone10 (gf: rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 -> rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9) :=
forall r r'(LE: r <10= r'), gf r <10== gf r'.

Lemma monotone10_union (gf gf': rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 -> rel10 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9)
(MON1: monotone10 gf)
(MON2: monotone10 gf'):
monotone10 (gf \11/ gf').