Nuprl Lemma : chain-path-member-not-input 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 loc(x) << loc(y (((y  In)))))) 
latex


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

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