es:ES, Cmd:Type, In:AbsInterface(Cmd), isupdate:(Cmd), Sys, Out:AbsInterface(Top).
(E(In) r E(Sys))
 (f:sys-antecedent(es;Sys).
 (e:E(In). f(e) = e  E)
  (chain:(E(Sys)(Id List)).
  chain-consistent(f;chain)
   (x, y:E(Sys).
   x is f*(y)
    (j:Id.
    loc(x) << j
     j <<= loc(y)
     (i:Id. loc(x) <<= i  i << j  cr-fails-before(es; Sys; chain; i; j))
     (e:E(Sys). (loc(e) = j & e is f*(y) & x is f*(e))))))) 

latex

Up	abstract chain replication
Definitions	s = t, t  T, ES, Type, AbsInterface(A), , x:AB(x), sys-antecedent(es;Sys), E(X), <a, b>, E, x:A. B(x), type List, chain-consistent(f;chain), x:A  B(x), b, left + right, {x:A| B(x)} , x:A. B(x), Id, P  Q, a < b, A, P  Q, P & Q, hd(l), L1  L2, e loc e' , adjacent(T;L;x;y), (x  l), no_repeats(T;l), Top, f(a), e c e', a:A fp B(a), strong-subtype(A;B), , !Void(), False, y is f*(x), f**(e), y=f*(x) via L, Atom$n, x before y  l, x << y, x <<= y, cr-fails-before(es; Sys; chain; x; y), loc(e), {T}, kind(e), Knd, first(e), (e <loc e'), s ~ t, SQType(T), let x,y = A in B(x;y), t.1, case b of inl(x) => s(x) | inr(y) => t(y), if b then t else f fi , e  X, source(l), destination(l), es-init(es;e), P  Q, P  Q, isrcv(e), es-first-from(es;e;l;tg), isrcv(k), lastchange(x;e), (last change to x before e), last(L), True, T, A c B, {i..j}, , IdLnk, a = b, x.A(x), x. t(x), locl(a), x,y. t(x;y), EqDecider(T), Unit, EOrderAxioms(E; pred?; info), EState(T), kindcase(k; a.f(a); l,t.g(l;t) ), Msg(M), , val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), e < e', r  s, constant_function(f;A;B), loc(e), kind(e), SWellFounded(R(x;y)), pred!(e;e'), x:A.B(x), S  T, suptype(S; T), first(e), pred(e), Dec(P), l_disjoint(T;l1;l2), MaName, (e < e'), e<e'.P(e), ee'.P(e), e<e'. P(e), ee'.P(e), e[e1,e2).P(e), e[e1,e2).P(e), e[e1,e2].P(e), e[e1,e2].P(e), e(e1,e2].P(e), , A  B, Atom, x,y:A//B(x;y), b | a, a ~ b, |p|, a  b, a <p b, |g|, a < b, x f y, |r|, xL. P(x), (xL.P(x)), , r < s, q-rel(r;x), Outcome, dstype(TypeNames; d; a), , ||as||, i  j < k, #$n, [], [car / cdr], A List, l[i], increasing(f;k), X(e), x  dom(f)
Lemmas	chain-order-le transitivity, chain-order-implies-before, before-adjacent2, sublist wf, es-locl wf, es-locl-iff, adjacent wf, es-le-loc, es-le wf, increasing wf, length wf nat, select wf, length wf1, int seg wf, le wf, chain-consistent-member, chain-consistent-fails-before, fun-connected transitivity, decidable equal es-E-interface, chain-path-ordered, fun-connected-step, decidable wf, decidable equal Id, chain-order transitivity, chain-order-antireflexive, kind wf, loc wf, first wf, pred! wf, strongwellfounded wf, es-is-interface wf, es-causle wf, es-interface wf, top wf, constant function wf, bool wf, qle wf, cless wf, val-axiom wf, rationals wf, nat wf, Msg wf, kindcase wf, Knd wf, EState wf, EOrderAxioms wf, IdLnk wf, unit wf, deq wf, chain-consistent wf, fun-connected-induction, all functionality wrt iff, implies functionality wrt iff, exists functionality wrt iff, and functionality wrt iff, assert-eq-id, eq id wf, es-first wf, l before wf, chain-order-le wf, cr-fails-before wf, chain-order wf, fun-path wf, fun-connected weakening eq, fun-connected wf, event system wf, true wf, squash wf, iff wf, rev implies wf, es-isrcv-loc, Id sq, es-loc-pred, false wf, guard wf, Id wf, es-loc wf, not wf, es-E-interface-subtype rel, assert wf, es-E wf, member wf, es-E-interface wf, sys-antecedent wf, subtype rel wf