Nuprl Lemma : chain-consistent-out-continuity 13,45

es:ES, Cmd:Type, In:AbsInterface(Cmd), isupdate:(Cmd), SysOut:AbsInterface(Top).
(E(Inr E(Sys))
 (f:sys-antecedent(es;Sys).
 (e:E(In). f(e) = e  E)
  (chain:(E(Sys)(Id List)).
  chain-consistent(f;chain)
   (xy:E(Sys).
   x is f*(y)
    (E(Outr E(Sys))
    (e':E(In).
    ((isupdate(In(e'))))
     (z:E(Sys). (y loc z  & ((z  Out))))
     loc(x) << loc(e')
     (e:E(Sys)
     ((loc(e) = loc(e' Id
     (& ((loc(f(e)) = loc(e Id))
     (e is f*(y)
     (x is f*(e))))))) 
latex


Upabstract chain replication
Definitionst  T, s = t, x:AB(x), x:AB(x), E(X), ES, Type, AbsInterface(A), sys-antecedent(es;Sys), chain-consistent(f;chain), y is f*(x), , <ab>, E, type List, x:A  B(x), x:AB(x), P  Q, b, left + right, {x:AB(x)} , Id, P  Q, a < b, A, P & Q, hd(l), L1  L2, e loc e' , adjacent(T;L;x;y), (x  l), no_repeats(T;l), y=f*(x) via L, False, Top, f(a), loc(e), x <<= y, x << y, X(e), e  X, , let x,y = A in B(x;y), t.1, a:A fp B(a), strong-subtype(A;B), case b of inl(x) => s(x) | inr(y) => t(y), if b then t else f fi , (e <loc e'), Unit, ff, inr x , tt, inl x , True, A c B, Atom$n, x before y  l, e c e', !Void(), f**(e), , l[i], {T}, source(l), destination(l), es-init(es;e), P  Q, P  Q, isrcv(e), kind(e), es-first-from(es;e;l;tg), isrcv(k), lastchange(x;e), (last change to x before e), last(L), {i..j}, , x  dom(f), EqDecider(T), IdLnk, EOrderAxioms(Epred?info), EState(T), Knd, xt(x), x,yt(x;y), kindcase(ka.f(a); l,t.g(l;t) ), Msg(M), val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), e < e', r  s, constant_function(f;A;B), f(x)?z, T
Lemmassquash wf, chain-order-in-out, chain-consistent-continuity, constant function wf, qle wf, cless wf, val-axiom wf, rationals wf, nat wf, Msg wf, kindcase wf, Knd wf, EState wf, EOrderAxioms wf, IdLnk wf, deq wf, event system wf, es-E-interface-subtype rel, chain-consistent wf, fun-path wf, chain-order-le wf, fun-connected wf, iff wf, rev implies wf, es-isrcv-loc, es-le-loc, es-loc-pred, not wf, fun-connected weakening eq, sys-antecedent wf, l before wf, Id wf, chain-order wf, es-loc wf, es-locl wf, es-le wf, true wf, false wf, es-interface wf, btrue wf, bfalse wf, unit wf, bool wf, top wf, member wf, subtype rel wf, es-interface-val wf2, es-E wf, assert wf, es-is-interface wf, es-E-interface wf

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