Nuprl Lemma : R-state-var-compat 11,40

i:Id, ds:fpf(Id; x.Type), da:fpf(Knd; k.Type), x:Id, T:Type, ks:(Knd List), tr:(k:{k:Knd| 
i:Id, ds:fpf(Id; x.Type), da:fpf(Knd; k.Type), x:Id, T:Type, ks:(Knd List), tr:(k:{(k  ks)} 
i:Id, ds:fpf(Id; x.Type), da:fpf(Knd; k.Type), x:Id, T:Type, ks:(Knd List), tr:(decl-state(ds)
i:Id, ds:fpf(Id; x.Type), da:fpf(Knd; k.Type), x:Id, T:Type, ks:(Knd List), tr:(ma-valtype(dak)
i:Id, ds:fpf(Id; x.Type), da:fpf(Knd; k.Type), x:Id, T:Type, ks:(Knd List), tr:(TT).
((fpf-dom(id-deq; xds)))
 (A:es_realizer{i:l}. 
 R-Feasible{i:l}
 R-Feasible(A)
  ((R-occurs(Aix)))
  fpf-compatible(Id; x.Type; id-deq; ds; R-ds(Ai))
  fpf-compatible(Knd; k.Type; Kind-deq; da; R-da(Ai))
  l_all(ks;
  l_all(Knd;
  l_all(k.((isrcv(k))
  l_all( subtype_rel(fpf-cap(R-da(A; source(lnk(k))); Kind-deq; k; void); ma-valtype(dak))))
  l_all(ks; Knd; k.(fpf-dom(Kind-deq; kda)))
  (k:Knd. (k  ks ((write-restricted(Aik))))
  (y:Id. 
  (fpf-dom(id-deq; y; fpf-join(id-deq; ds; fpf-single(xT))))
   ((read-restricted(Aiy))))
  R-compat{i:l}
  R-compat(R-state-var(idsdaxTkstr); A)) 
latex


Definitionsfpf-cap(feqxz), ma-valtype(dak), t.2, fpf-single(xv), fpf-ap(feqx), guard(T), sq_type(T), P  Q, P  Q, fpf-compatible(Aa.B(a); eqfg), A, ff, tt, if b then t else f fi , decl-type{i:l}(dsx), decl-state(ds), prop{i:l}, xt(x), t  T, top, P  Q, R-state-var(idsdaxTkstr), l_all(LTx.P(x)), es_realizer{i:l}, P  Q, fpf(Aa.B(a)), x:AB(x), False, Unit, , x(s),
LemmasKnd sq, fpf-single-dom, and functionality wrt iff, dom-R-ds-occurs, fpf-compatible-single2, fpf-compatible-join2, fpf-cap-single1, assert of bnot, eqff to assert, bnot wf, iff transitivity, eqtt to assert, fpf-join-cap-sq, fpf-cap-join-subtype, subtype rel self, subtype rel dep function, Id wf, id-deq wf, bool wf, finite-prob-space wf, fpf wf, IdLnk wf, unit wf, R-Feasible wf, R-occurs wf, R-ds wf, Kind-deq wf, Knd wf, fpf-compatible wf, lnk wf, lsrc wf, R-da wf, fpf-cap wf, fpf-trivial-subtype-top, write-restricted wf, read-restricted wf, not wf, fpf-single wf, top wf, fpf-dom wf, not-R-occurs-frame-compat, l member wf, isrcv wf, assert wf, not-R-occurs-effect-compat, decl-type wf, rationals wf, decl-state wf, ma-valtype wf, fpf-single wf3, fpf-join wf, Reffect wf, R-compat-Rall2, R-compat-Rplus-sq

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