es:ES, Cmd:Type, In:AbsInterface(Cmd), isupdate:(Cmd), Sys, Out:AbsInterface(Top).
(E(In) r E(Sys))
 (f:sys-antecedent(es;Sys), chain:(E(Sys)(Id List)).
 chain-consistent(f;chain)  (x, y, z:Id. x <<= y  y << z  x << z)) 

latex

Up	abstract chain replication
Definitions	x <<= y, #$n, ||as||, loc(e), P  Q, P  Q, a = b, x before y  l, x << y, Atom$n, no_repeats(T;l), (x  l), adjacent(T;L;x;y), e loc e' , L1  L2, hd(l), a < b, x:A. B(x), chain-consistent(f;chain), e c e', sys-antecedent(es;Sys), E(X), {x:A| B(x)} , e  X, AbsInterface(A), E, P & Q, x. t(x), x.A(x), pred(e), <a, b>, A, first(e), suptype(S; T), S  T, Top, x:A.B(x), !Void(), x,y. t(x;y), pred!(e;e'), , SWellFounded(R(x;y)), constant_function(f;A;B), b, , e < e', r  s, val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), , type List, Msg(M), kind(e), loc(e), Knd, kindcase(k; a.f(a); l,t.g(l;t) ), EOrderAxioms(E; pred?; info), x:A  B(x), IdLnk, Unit, EqDecider(T), Type, P  Q, strong-subtype(A;B), , Id, f(a), a:A fp B(a), EState(T), ES, x:A. B(x), x:AB(x), t  T, s = t, P  Q, left + right
Lemmas	chain-order transitivity, event system wf, subtype rel wf, EState wf, Id wf, rationals wf, member wf, strongwellfounded wf, pred! wf, unit wf, top wf, first wf, assert wf, not wf, loc wf, constant function wf, IdLnk wf, kindcase wf, Knd wf, bool wf, qle wf, cless wf, val-axiom wf, nat wf, Msg wf, kind wf, EOrderAxioms wf, deq wf, es-E wf, es-is-interface wf, es-E-interface wf, es-interface wf, sys-antecedent wf, es-causle wf, chain-consistent wf, chain-order wf, eq id wf, assert-eq-id, rev implies wf, iff wf, or functionality wrt iff