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 2 *)
(** 1 Mutual Coinduction *)
Section Arg2_1.
Definition monotone2 T0 T1 (gf: rel2 T0 T1 -> rel2 T0 T1) :=
forall x0 x1 r r' (IN: gf r x0 x1) (LE: r <2= r'), gf r' x0 x1.
Variable T0 : Type.
Variable T1 : forall (x0: @T0), Type.
Variable gf : rel2 T0 T1 -> rel2 T0 T1.
Implicit Arguments gf [].

(* Specifications: *)
Theorem paco2_acc: forall
l r (OBG: forall rr (INC: r <2= rr) (CIH: l <_paco_2= rr), l <_paco_2= paco2 gf rr),
l <2= paco2 gf r.
Theorem paco2_mon: monotone2 (paco2 gf).
Theorem paco2_2_1_acc: forall
l r_0 r_1 (OBG: forall rr (INC: r_1 <2= rr) (CIH: l <_paco_2= rr), l <_paco_2= paco2_2_1 gf_0 gf_1 r_0 rr),
l <2= paco2_2_1 gf_0 gf_1 r_0 r_1.
Theorem paco2_2_0_mon: monotone2_2 (paco2_2_0 gf_0 gf_1).
Theorem paco2_3_1_acc: forall
l r_0 r_1 r_2 (OBG: forall rr (INC: r_1 <2= rr) (CIH: l <_paco_2= rr), l <_paco_2= paco2_3_1 gf_0 gf_1 gf_2 r_0 rr r_2),
l <2= paco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco2_3_2_acc: forall
l r_0 r_1 r_2 (OBG: forall rr (INC: r_2 <2= rr) (CIH: l <_paco_2= rr), l <_paco_2= paco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 rr),
l <2= paco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco2_3_0_mon: monotone2_3 (paco2_3_0 gf_0 gf_1 gf_2).