es:ES, Cmd:Type, isupdate:(Cmd), In:AbsInterface(Cmd), Out:AbsInterface(Top),
expl:(E(Out)(E(In) List)).
consistent-updates(es;In;Out;Cmd;isupdate;expl)   

latex

Up	abstract chain replication
Definitions of Statement	consistent-updates(es;In;Out;Cmd;isupdate;expl)
Definitions	s = t, t  T, x:AB(x), x:A. B(x), ES, EState(T), a:A fp B(a), f(a), Id, , strong-subtype(A;B), P  Q, Type, EqDecider(T), Unit, left + right, IdLnk, x:A  B(x), EOrderAxioms(E; pred?; info), kindcase(k; a.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', , b, constant_function(f;A;B), SWellFounded(R(x;y)), , pred!(e;e'), x,y. t(x;y), !Void(), x:A.B(x), Top, S  T, suptype(S; T), first(e), A, <a, b>, pred(e), x.A(x), x. t(x), P & Q, E, AbsInterface(A), e  X, {x:A| B(x)} , E(X), updates(L), X(e), case b of inl(x) => s(x) | inr(y) => t(y), True, False, l1  l2, as @ bs, P  Q, consistent-updates(es;In;Out;Cmd;isupdate;expl)
Lemmas	es-interface-val wf2, false wf, append wf, iseg wf, updates of wf, true 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