Nuprl Lemma : decidable__exists-es-p-le-pred 11,40

es:ES, P:(E), e:E. (e:E. Dec(P(e)))  Dec(a:E. (es-p-le-pred(es;P)(e,a))) 
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Definitionss = t, t  T, x:AB(x), x:AB(x), ES, a:A fp B(a), x:A  B(x), Type, EqDecider(T), Unit, left + right, IdLnk, Id, EOrderAxioms(Epred?info), f(a), 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, P  Q, , b, constant_function(f;A;B), P & Q, Top, strong-subtype(A;B), E, let x,y = A in B(x;y), , Dec(P), t.1, P  Q, A, loc(e), <ab>, loc(e), kind(e), (e <loc e'), (e < e'), (x  l), x:A.B(x), a = b, P  Q, P  Q, locl(a), e@iP(e), {x:AB(x)} , x(s), ee'.P(e), x.A(x), A c B, ee'.P(e), es-p-le-pred(es;P), x:AB(x), False, a < b, A  B, {i..j}, 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, l_disjoint(T;l1;l2), e loc e' , e c e', e<e'.P(e), e<e'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)
Lemmases-p-le-pred wf, decidable existse-le, decidable cand, alle-le wf, decidable alle-le, es-E wf, iff wf, rev implies wf, assert-eq-id, decidable implies better, decidable es-locl, not wf, decidable wf, decidable not, es-locl wf, es-loc wf, member wf, top wf, constant function wf, assert 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, subtype rel wf

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