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 1 *)
(** 1 Mutual Coinduction *)
Section Arg1_1.
Definition monotone1 T0 (gf: rel1 T0 -> rel1 T0) :=
forall x0 r r' (IN: gf r x0) (LE: r <1= r'), gf r' x0.
Variable T0 : Type.
Variable gf : rel1 T0 -> rel1 T0.
Implicit Arguments gf [].

(* Specifications: *)
Theorem paco1_acc: forall
l r (OBG: forall rr (INC: r <1= rr) (CIH: l <_paco_1= rr), l <_paco_1= paco1 gf rr),
l <1= paco1 gf r.
Theorem paco1_mon: monotone1 (paco1 gf).
Theorem paco1_2_1_acc: forall
l r_0 r_1 (OBG: forall rr (INC: r_1 <1= rr) (CIH: l <_paco_1= rr), l <_paco_1= paco1_2_1 gf_0 gf_1 r_0 rr),
l <1= paco1_2_1 gf_0 gf_1 r_0 r_1.
Theorem paco1_2_0_mon: monotone1_2 (paco1_2_0 gf_0 gf_1).
Theorem paco1_3_1_acc: forall
l r_0 r_1 r_2 (OBG: forall rr (INC: r_1 <1= rr) (CIH: l <_paco_1= rr), l <_paco_1= paco1_3_1 gf_0 gf_1 gf_2 r_0 rr r_2),
l <1= paco1_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco1_3_2_acc: forall
l r_0 r_1 r_2 (OBG: forall rr (INC: r_2 <1= rr) (CIH: l <_paco_1= rr), l <_paco_1= paco1_3_2 gf_0 gf_1 gf_2 r_0 r_1 rr),
l <1= paco1_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco1_3_0_mon: monotone1_3 (paco1_3_0 gf_0 gf_1 gf_2).