Nuprl Lemma : chain-path-ordered-same-loc 13,45

es:ES, Sys:AbsInterface(Top), f:sys-antecedent(es;Sys), xy:E(Sys).
x is f*(y (loc(x) = loc(y Id)  x loc y  
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Upabstract chain replication
Definitionss = t, t  T, x:AB(x), x:AB(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(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', , b, 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), A, <ab>, pred(e), x.A(x), xt(x), P & Q, E, sys-antecedent(es;Sys), AbsInterface(A), E(X), e c e', {x:AB(x)} , e  X, y is f*(x), y=f*(x) via L, let x,y = A in B(x;y), t.1, x:AB(x), hd(l), loc(e), Atom$n, e loc e' , (e <loc e'), X(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, P  Q, lastchange(x;e), es-init(es;e), True, a = b, locl(a), (x  l), f**(e), sender(e), T, 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), 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, {T}
Lemmassq stable from decidable, decidable es-causle, fun-connected-causle, es-le-causle, es-E-interface-subtype rel, es-interface wf, iff wf, rev implies wf, assert-eq-id, es-causle-le, es-causl wf, es-locl wf, es-le wf, es-loc wf, fun-path wf, fun-connected wf, es-is-interface wf, es-causle wf, es-E-interface wf, sys-antecedent 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

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