Require Export VST.concurrency.paco.src.paconotation VST.concurrency.paco.src.pacotac VST.concurrency.paco.src.pacodef VST.concurrency.paco.src.pacotacuser.
Set Implicit Arguments.
(** ** Predicates of Arity 4 *)
(** 1 Mutual Coinduction *)
Section Arg4_1.
Definition monotone4 T0 T1 T2 T3 (gf: rel4 T0 T1 T2 T3 -> rel4 T0 T1 T2 T3) :=
forall x0 x1 x2 x3 r r' (IN: gf r x0 x1 x2 x3) (LE: r <4= r'), gf r' x0 x1 x2 x3.
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 gf : rel4 T0 T1 T2 T3 -> rel4 T0 T1 T2 T3.
Implicit Arguments gf [].

(* Specifications: *)
Theorem paco4_acc: forall
l r (OBG: forall rr (INC: r <4= rr) (CIH: l <_paco_4= rr), l <_paco_4= paco4 gf rr),
l <4= paco4 gf r.
Theorem paco4_mon: monotone4 (paco4 gf).
Theorem paco4_2_1_acc: forall
l r_0 r_1 (OBG: forall rr (INC: r_1 <4= rr) (CIH: l <_paco_4= rr), l <_paco_4= paco4_2_1 gf_0 gf_1 r_0 rr),
l <4= paco4_2_1 gf_0 gf_1 r_0 r_1.
Theorem paco4_2_0_mon: monotone4_2 (paco4_2_0 gf_0 gf_1).
Theorem paco4_3_1_acc: forall
l r_0 r_1 r_2 (OBG: forall rr (INC: r_1 <4= rr) (CIH: l <_paco_4= rr), l <_paco_4= paco4_3_1 gf_0 gf_1 gf_2 r_0 rr r_2),
l <4= paco4_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco4_3_2_acc: forall
l r_0 r_1 r_2 (OBG: forall rr (INC: r_2 <4= rr) (CIH: l <_paco_4= rr), l <_paco_4= paco4_3_2 gf_0 gf_1 gf_2 r_0 r_1 rr),
l <4= paco4_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco4_3_0_mon: monotone4_3 (paco4_3_0 gf_0 gf_1 gf_2).