Nuprl Lemma : cr-explanation-connected 13,45

es:ES, Cmd:Type, In:AbsInterface(Cmd), Sys:AbsInterface(Top).
(E(Inr E(Sys))
 (f:sys-antecedent(es;Sys).
 (u:E(Sys). (f(u) = u  E)  ((u  In)))
  (ea:E(Sys).
  a is f*(e)
   (cr-explanation{i:l}
   (cr-explanation(esSysfa)
   (=
   (cr-explanation{i:l}
   (cr-explanation(esSysfe)
   ( (E(In) List)))) 
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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, AbsInterface(A), e  X, {x:AB(x)} , E(X), sys-antecedent(es;Sys), e c e', ff, inr x , tt, inl x , False, True, case b of inl(x) => s(x) | inr(y) => t(y), let x,y = A in B(x;y), t.1, if b then t else f fi , y is f*(x), y=f*(x) via L, cr-explanation{i:l}(esSysfe), x  dom(f), x:AB(x), hd(l), (x  l), f**(e), es-prior-fixedpoints{i:l}(esSysfe), P  Q, (e < e'), P  Q, P  Q, f(x)?z, T, s ~ 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
Lemmases-fix-connected, sq stable all, sq stable from decidable, decidable es-causle, es-causl wf, es-prior-fixedpoints-fix, es-prior-fixedpoints wf, squash wf, fun-path wf, fun-connected wf, es-E-interface-subtype rel, true wf, false wf, btrue wf, bfalse wf, es-causle wf, sys-antecedent 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

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