Nuprl Lemma : update-antecedent-lemma1 11,40

es:ES, Cmd:Type, Sys:AbsInterface(chain_sys(Cmd)), Config:AbsInterface(chain_config()),
u:({e:E(Sys)| csupdate?(Sys(e))} {e:E| ((e  Sys))  ((e  Config))} ).
update-antecedent{i:l}(es;Cmd;Sys;Config;u)
 Sys  Config = 0
 (e:E(Sys(valid)).
 (csupdate?(Sys(e)))  (((u(e))  Config))  (u(e E(prior(Sys(valid))))) 
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Definitionss = t, x:AB(x), x:AB(x), E, {x:AB(x)} , a:A fp B(a), b, left + right, P  Q, f(a), strong-subtype(A;B), P  Q, ||as||, ccsucc-num(x), ES, Type, X  Y = 0, prior(X), a < b, loc(e), X(e), ccsucc-id(x), Id, cmd-history(e), nth_tl(n;as), csupdate-cmds(x), type List, x:A  B(x), P & Q, let x = a in b(x), A c B, update-antecedent{i:l}(es;Cmd;Sys;Config;u), case b of inl(x) => s(x) | inr(y) => t(y), if b then t else f fi , chain_sys(Cmd), chain_config(), , csupdate?(x), e  X, Unit, tt, inr x , "$token", ff, inl x , Atom, True, False, , x:AB(x), (e < e'), <ab>, chain_sys_ind(x;cmd.input(cmd);from,cmds.update(from;cmds)), e < e', (e <loc e'), valid-sys(es;Config;Sys;e), A, ccsucc?(x), (x  l), x  dom(f), Void, x:A.B(x), P  Q, P  Q, f  g, f(x)?z, vartype(i;x), state@i, State(ds), State(ds), {T}, EqDecider(T), IdLnk, EOrderAxioms(Epred?info), EState(T), Knd, xt(x), x,yt(x;y), kindcase(ka.f(a); l,t.g(l;t) ), Msg(M), , , val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), r  s, constant_function(f;A;B), let x,y = A in B(x;y), T, , Sys(valid), Top, AbsInterface(A), t  T, E(X), x.A(x), sys-cmds(x), t.1, i  j , , Outcome, A  B, #$n, e(e1,e2].P(e), @e(xv), (last change to x before e), pred(e), e loc e' 
Lemmasis-sys-valid, not wf, nonempty-cmd-history, es-causl wf, es-locl wf, es-is-prior-interface, non neg length, length wf1, cmd-history wf, es-interface-val wf2, ccsucc-num wf, false wf, es-is-interface wf, sys-valid-subtype, sys-valid wf, squash wf, subtype rel function, 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, subtype rel sum, update-antecedent wf, chain config wf, es-interface-disjoint wf, true wf, top wf, es-interface wf, chain sys wf, Id wf, bfalse wf, btrue wf, unit wf, bool wf, member wf, es-E-interface wf, assert wf, es-E wf, subtype rel wf

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