Nuprl Lemma : chain-consistent-prior-to-input 13,45

es:ES, Cmd:Type, In:AbsInterface(Cmd), isupdate:(Cmd), SysOut:AbsInterface(Top).
(E(Inr E(Sys))
 (f:sys-antecedent(es;Sys), chain:(E(Sys)(Id List)).
 chain-consistent(f;chain)
  (a:E(In), b:E(Sys).
  (loc(b) = loc(a Id)
   (((b  In)))
   ((isupdate(In(a))))
   ((loc(f(b)) = loc(b Id))
   b loc prior(Sys)(a) )) 
latex


Upabstract chain replication
DefinitionsE(X), chain-consistent(f;chain), s = t, A, b, sys-antecedent(es;Sys), x:AB(x), x:AB(x), P  Q, t  T, ES, EState(T), a:A fp B(a), f(a), Id, , strong-subtype(A;B), Type, EqDecider(T), Unit, left + right, IdLnk, x:A  B(x), EOrderAxioms(Epred?info), kindcase(ka.f(a); l,t.g(l;t) ), Knd, loc(e), kind(e), Msg(M), type List, , val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), r  s, e < e', , constant_function(f;A;B), SWellFounded(R(x;y)), , pred!(e;e'), x,yt(x;y), !Void(), x:A.B(x), Top, S  T, suptype(ST), first(e), <ab>, pred(e), x.A(x), xt(x), P & Q, E, AbsInterface(A), e  X, {x:AB(x)} , e c e', x:AB(x), P  Q, a < b, hd(l), L1  L2, e loc e' , adjacent(T;L;x;y), (x  l), no_repeats(T;l), let x,y = A in B(x;y), t.1, loc(e), Atom$n, ff, inr x , tt, inl x , False, True, case b of inl(x) => s(x) | inr(y) => t(y), X(e), if b then t else f fi , (e <loc e'), e(e1,e2].P(e), @e(xv), (last change to x before e), A c B, pred(e), (e < e'), P  Q, P  Q, lastchange(x;e), es-init(es;e), a = b, prior(X), x  dom(f), locl(a), ||as||, #$n, Dec(P), e<e'.P(e), ee'.P(e), e<e'P(e), ee'.P(e), e[e1,e2).P(e), e[e1,e2).P(e), e[e1,e2].P(e), e[e1,e2].P(e), e(e1,e2].P(e), T, b | a, a ~ b, a  b, a <p b, a < b, x f y, xLP(x), (xL.P(x)), y is f*(x), r < s, q-rel(r;x), Outcome, l_disjoint(T;l1;l2), SqStable(P), a =!x:TQ(x), InvFuns(A;B;f;g), Inj(A;B;f), IsEqFun(T;eq), Refl(T;x,y.E(x;y)), Sym(T;x,y.E(x;y)), Trans(T;x,y.E(x;y)), AntiSym(T;x,y.R(x;y)), Connex(T;x,y.R(x;y)), CoPrime(a,b), Ident(T;op;id), Assoc(T;op), Comm(T;op), Inverse(T;op;id;inv), BiLinear(T;pl;tm), IsBilinear(A;B;C;+a;+b;+c;f), IsAction(A;x;e;S;f), Dist1op2opLR(A;1op;2op), fun_thru_1op(A;B;opa;opb;f), FunThru2op(A;B;opa;opb;f), Cancel(T;S;op), monot(T;x,y.R(x;y);f), IsMonoid(T;op;id), IsGroup(T;op;id;inv), IsMonHom{M1,M2}(f), a  b, IsIntegDom(r), IsPrimeIdeal(R;P), f  g, {i..j}
Lemmases-prior-interface-val, es-is-prior-interface, sq stable from decidable, decidable assert, decidable es-locl, es-le-not-locl, es-le wf, not functionality wrt iff, iff wf, rev implies wf, assert-eq-id, eq id wf, es-causle-le, es-le-prior-interface-val, es-causl wf, es-locl wf, es-E-interface-subtype rel, es-interface-val wf2, true wf, false wf, btrue wf, bfalse wf, es-loc wf, chain-consistent wf, es-causle wf, sys-antecedent wf, es-interface wf, es-E-interface wf, es-is-interface wf, es-E wf, deq wf, EOrderAxioms wf, kind wf, Msg wf, nat wf, val-axiom wf, cless wf, qle wf, bool wf, Knd wf, kindcase wf, IdLnk wf, constant function wf, loc wf, not wf, assert wf, first wf, top wf, unit wf, pred! wf, strongwellfounded wf, member wf, rationals wf, Id wf, EState wf, subtype rel wf, event system wf, chain-consistent-after-input

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