Nuprl Lemma : es-local-le-pred-property 11,40

es:ES, P:(E), e:E.
(((e  es-local-le-pred{i:l}(es;P)))  (a:E. (a loc e  & ((P(a))))))
& (((e  es-local-le-pred{i:l}(es;P)))
& ( (es-local-le-pred{i:l}(es;P)(eloc e 
& ( & ((P(es-local-le-pred{i:l}(es;P)(e))))
& ( & (e'':E. e'' loc e   (es-local-le-pred{i:l}(es;P)(e) <loc e'' (((P(e''))))))) 
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DefinitionsES, x:A  B(x), x:AB(x), x:AB(x), E, AbsInterface(A), x:AB(x), s = t, f(a), b, e loc e' , P & Q, A, (e <loc e'), P  Q, P  Q, t  T, Type, , <ab>, es-interface-le-pred-bool, X(e), x.A(x), es-p-le-pred(es;P), e  X, P  Q, , let x,y = A in B(x;y), t.1, left + right, case b of inl(x) => s(x) | inr(y) => t(y), if b then t else f fi , {x:AB(x)} , E(X), a:A fp B(a), strong-subtype(A;B), EqDecider(T), Unit, IdLnk, Id, EOrderAxioms(Epred?info), EState(T), Knd, xt(x), x,yt(x;y), kindcase(ka.f(a); l,t.g(l;t) ), Msg(M), type List, , , val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), e < e', r  s, constant_function(f;A;B), Top, ff, inr x , tt, inl x , False, True, A c B, loc(e), kind(e), SWellFounded(R(x;y)), pred!(e;e'), Void, x:A.B(x), S  T, suptype(ST), first(e), pred(e), es-local-le-pred{i:l}(es;P), WellFnd{i}(A;x,y.R(x;y)), P  Q, Dec(P), b | a, a ~ b, a  b, a <p b, a < b, x f y, xLP(x), (xL.P(x)), r < s, q-rel(r;x), Outcome, (x  l), l_disjoint(T;l1;l2), (e < e'), e c 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), {T}, x(s), first(e), lastchange(x;e), es-init(es;e), pred(e), s ~ t, SQType(T)
Lemmasguard wf, es-locl transitivity1, all functionality wrt iff, implies functionality wrt iff, es-causl wf, es-pred-locl, es-causle-le, es-le-pred, es-pred wf, es-locl-iff, es-le weakening, es-le weakening eq, es-locl transitivity2, es-locl irreflexivity, es-locl-wellfnd, decidable assert, es-interface-le-pred-bool, kind wf, loc wf, first wf, pred! wf, strongwellfounded wf, true wf, false wf, btrue wf, bfalse wf, es-p-le-pred wf, es-interface-val wf, es-interface wf, es-interface-val wf2, 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, Id wf, IdLnk wf, unit wf, deq wf, event system wf, member wf, es-E-interface wf, subtype rel wf, not wf, es-locl wf, iff wf, es-is-interface wf, rev implies wf, es-E wf, es-le wf, assert wf

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