Nuprl Lemma : es-le-before-partition 11,40

es:ES, ea:E. a loc e   (es-le-before(es;e) = (before(a) @ [ae])  (E List)) 
latex


Definitionsleft + right, P  Q, e loc e' , E, type List, [], t  T, A List, s = t, x:AB(x), x:AB(x), [car / cdr], {x:AB(x)} , before(e), as @ bs, , P  Q, (e <loc e'), ES, WellFnd{i}(A;x,y.R(x;y)), x:A  B(x), a:A fp B(a), [ee'], <ab>, strong-subtype(A;B), x.A(x), {T}, xt(x), es-le-before(es;e), b, f(a), x(s), let x,y = A in B(x;y), t.1, e < e', loc(e), Id, P & Q, (e < e'), , A, P  Q, False, P  Q, e c e', es-init(es;e), True, Void, pred(e), Type, EqDecider(T), Unit, IdLnk, EOrderAxioms(Epred?info), EState(T), Knd, x,yt(x;y), kindcase(ka.f(a); l,t.g(l;t) ), Msg(M), , , val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), r  s, constant_function(f;A;B), Top, loc(e), kind(e), A c B, T, s ~ t, SQType(T), A  B, i  j , ||as||, first(e), ff, b, tt, x  dom(f), case b of inl(x) => s(x) | inr(y) => t(y), if b then t else f fi , p =b q, i <z j, i j, (i = j), x =a y, null(as), a < b, x f y, a < b, [d], eq_atom$n(x;y), q_le(r;s), q_less(a;b), qeq(r;s), a = b, a = b, deq-member(eq;x;L), e = e', p  q, p  q, p q,
Lemmases-first-implies, eqtt to assert, iff transitivity, eqff to assert, assert of bnot, es-first wf, bnot wf, es-interval-partition, es-interval-eq, non neg length, cons one one, guard wf, iff wf, rev implies wf, append assoc, true wf, squash wf, es-le weakening eq, 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, member wf, subtype rel wf, es-pred wf, es-causl wf, Id wf, es-pred-locl, es-causle-le, es-le-pred, not wf, false wf, assert wf, es-locl-iff, event system wf, es-locl-wellfnd, es-interval wf, es-locl wf, es-le wf, append wf, es-before wf, es-E wf

origin