use "-n>" in the world_prop signature

lib/ModuRes/Finmap.v

@@ -470,7 +470,7 @@ Section FinDom.
     Context {V} `{cV : pcmType V}.
 
     Definition equiv_fd (f1 f2 : K -f> V) := forall k, f1 k == f2 k.
-    Global Program Instance type_findom : Setoid (K -f> V) := mkType equiv_fd.
+    Global Program Instance type_findom : Setoid (K -f> V) | 5:= mkType equiv_fd.
     Next Obligation.
       split.
       - intros m k; reflexivity.
@@ -489,7 +489,7 @@ Section FinDom.
         | S _ => forall k, f1 k = n = f2 k
       end.
 
-    Global Program Instance metric_findom : metric (K -f> V) := mkMetr dist_fd.
+    Global Program Instance metric_findom : metric (K -f> V) | 5 := mkMetr dist_fd.
     Next Obligation.
       revert n; intros [| n] f1 f2 EQf g1 g2 EQg; [reflexivity |]; split;
       intros EQ k; [symmetry in EQf, EQg |]; rewrite EQf, EQg; apply EQ.
@@ -552,7 +552,7 @@ Section FinDom.
       fun n => Indom_lookup x (findom_t (σ (S n))) (proj2 (In_inlst _ _) (finmap_chain_dom _ _ _ HIn)).
 
     Program Instance finmap_chainx_cauchy (σ : chain (K -f> V)) {σc : cchain σ} x (HIn : x ∈ dom (σ 1)) :
-      cchain (finmap_chainx σ x HIn).
+      cchain (finmap_chainx σ x HIn) | 5.
     Next Obligation.
       unfold cchain; intros.
       assert (HT : Some (finmap_chainx σ x HIn i) = S n = Some (finmap_chainx σ x HIn j)); [| apply dist_mono, HT].
@@ -562,7 +562,7 @@ Section FinDom.
     Definition findom_lub (σ : chain (K -f> V)) (σc : cchain σ) : K -f> V :=
       findom_map _ _ (σ 1) (fun x HLu => compl (finmap_chainx σ x (proj1 (In_inlst _ _) HLu))).
 
-    Global Program Instance findom_cmetric : cmetric (K -f> V) := mkCMetr findom_lub.
+    Global Program Instance findom_cmetric : cmetric (K -f> V) | 5 := mkCMetr findom_lub.
     Next Obligation.
       intros [| n]; [exists 0; intros; exact I |].
       assert (HT : exists m, forall x, inlst x (dom (σ 1)) = true -> forall (X : inlst x (dom (σ 1)) = true) i,

lib/ModuRes/PreoMet.v

@@ -58,7 +58,7 @@ Section PUMMorphProps1.
 
   Definition PMEquiv (x y : T -m> U) := mu_morph x == mu_morph y.
 
-  Global Program Instance PMtypeM : Setoid (T -m> U) := mkType PMEquiv.
+  Global Program Instance PMtypeM : Setoid (T -m> U) | 5 := mkType PMEquiv.
   Next Obligation.
     split.
     - intros f x; simpl; reflexivity.
@@ -68,7 +68,7 @@ Section PUMMorphProps1.
 
   Definition PMDist n (f g : T -m> U) := (mu_morph f) = n = (mu_morph g).
 
-  Global Program Instance PMMetric : metric (T -m> U) := mkMetr PMDist.
+  Global Program Instance PMMetric : metric (T -m> U) | 5 := mkMetr PMDist.
   Next Obligation.
     intros f g EQfg h i EQhi; split; intros EQ x; [symmetry in EQfg, EQhi |]; rewrite (EQfg x), (EQhi x); apply EQ.
   Qed.
@@ -126,7 +126,7 @@ Section PUMMorphProps1.
     rewrite HSub; reflexivity.
   Qed.
 
-  Global Program Instance PMcmetric : cmetric (T -m> U) :=
+  Global Program Instance PMcmetric : cmetric (T -m> U) | 5 :=
     mkCMetr PMCompl.
   Next Obligation.
     apply (conv_cauchy (liftc mu_morph_ne σ)).

world_prop.v

@@ -4,6 +4,7 @@ Require Import ModuRes.PreoMet ModuRes.MetricRec ModuRes.CBUltInst.
 Require Import ModuRes.Finmap ModuRes.Constr.
 Require Import ModuRes.PCM ModuRes.UPred ModuRes.BI.
 
+
 (* This interface keeps some of the details of the solution opaque *)
 Module Type WORLD_PROP (Res : PCM_T).
   (* PreProp: The solution to the recursive equation. Equipped with a discrete order *)
@@ -15,17 +16,18 @@ Module Type WORLD_PROP (Res : PCM_T).
   (* Defines Worlds, Propositions *)
   Definition Wld       := nat -f> PreProp.
   Definition Props     := Wld -m> UPred Res.res.
-  
+
   (* Define all the things on Props, so they have names - this shortens the terms later *)
-  Instance Props_ty   : Setoid Props := _.
-  Instance Props_m    : metric Props := _.
-  Instance Props_cm   : cmetric Props := _.
-  Instance Props_preo : preoType Props := _.
-  Instance Props_pcm  : pcmType Props := _.
+  Instance Props_ty   : Setoid Props  | 1 := _.
+  Instance Props_m    : metric Props  | 1 := _.
+  Instance Props_cm   : cmetric Props | 1 := _.
+  Instance Props_preo : preoType Props| 1 := _.
+  Instance Props_pcm  : pcmType Props | 1 := _.
 
+  
   (* Establish the recursion isomorphism *)
-  Parameter ı  : PreProp -t> halve (cmfromType Props).
-  Parameter ı' : halve (cmfromType Props) -t> PreProp.
+  Parameter ı  : PreProp -n> halve (cmfromType Props).
+  Parameter ı' : halve (cmfromType Props) -n> PreProp.
   Axiom iso : forall P, ı' (ı P) == P.
   Axiom isoR: forall T, ı (ı' T) == T.
 End WORLD_PROP.