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 3 *)
(** 1 Mutual Coinduction *)
Section Arg3_1.
Definition monotone3 T0 T1 T2 (gf: rel3 T0 T1 T2 -> rel3 T0 T1 T2) :=
forall x0 x1 x2 r r' (IN: gf r x0 x1 x2) (LE: r <3= r'), gf r' x0 x1 x2.
Variable T0 : Type.
Variable T1 : forall (x0: @T0), Type.
Variable T2 : forall (x0: @T0) (x1: @T1 x0), Type.
Variable gf : rel3 T0 T1 T2 -> rel3 T0 T1 T2.
Implicit Arguments gf [].

(* Specifications: *)
Theorem paco3_acc: forall
l r (OBG: forall rr (INC: r <3= rr) (CIH: l <_paco_3= rr), l <_paco_3= paco3 gf rr),
l <3= paco3 gf r.
Theorem paco3_mon: monotone3 (paco3 gf).
Theorem paco3_2_1_acc: forall
l r_0 r_1 (OBG: forall rr (INC: r_1 <3= rr) (CIH: l <_paco_3= rr), l <_paco_3= paco3_2_1 gf_0 gf_1 r_0 rr),
l <3= paco3_2_1 gf_0 gf_1 r_0 r_1.
Theorem paco3_2_0_mon: monotone3_2 (paco3_2_0 gf_0 gf_1).
Theorem paco3_3_1_acc: forall
l r_0 r_1 r_2 (OBG: forall rr (INC: r_1 <3= rr) (CIH: l <_paco_3= rr), l <_paco_3= paco3_3_1 gf_0 gf_1 gf_2 r_0 rr r_2),
l <3= paco3_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco3_3_2_acc: forall
l r_0 r_1 r_2 (OBG: forall rr (INC: r_2 <3= rr) (CIH: l <_paco_3= rr), l <_paco_3= paco3_3_2 gf_0 gf_1 gf_2 r_0 r_1 rr),
l <3= paco3_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco3_3_0_mon: monotone3_3 (paco3_3_0 gf_0 gf_1 gf_2).