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2317 y FF(,)36 b(w)m(e)f(deriv)m(e)0 2467 y(from)c(Lemma)h(4.10)f(that) i FD(u)1052 2482 y Fy(j)1116 2467 y FB(!)1216 2431 y FC(\003)1216 2492 y(R)1307 2467 y FB(r)p FF(\()p FD(v)1475 2482 y Fy(j)1512 2467 y FF(\))1610 2411 y Fy(i)g FC(\003)1590 2467 y FB(!)1678 2483 y Fy(U)7 b Fz(\()p FC(R)p Fz(\))1880 2467 y FD(v)1927 2482 y Fy(j)1964 2467 y FF(.)43 b(If)33 b FD(u)2188 2482 y Fy(j)2251 2467 y FB(!)2351 2426 y Fz(+)2351 2494 y FC(R)2443 2467 y FB(r)p FF(\()p FD(v)2611 2482 y Fy(j)2648 2467 y FF(\),)f(then)h(the)g(deriv)-5 b(ation)313 2683 y FD(s)28 b FB(!)487 2642 y Fz(+)487 2710 y FC(R)579 2683 y FD(f)11 b FF(\()p FD(u)732 2698 y Fz(1)770 2683 y FD(;)17 b(:)g(:)g(:)f(;)h(u)1045 2698 y Fy(j)t FC(\000)p Fz(1)1171 2683 y FD(;)g FB(r)p FF(\()p FD(v)1383 2698 y Fy(j)1419 2683 y FF(\))p FD(;)g(u)1557 2698 y Fy(j)t Fz(+1)1683 2683 y FD(;)g(:)g(:)g(:)f(u)1914 2698 y Fy(m)1980 2683 y FF(\))28 b(=)f FD(t)2245 2627 y Fy(i)32 b FC(\003)2224 2683 y FB(!)2313 2698 y Fy(U)7 b Fz(\()p FC(R)p 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Fy(i)1683 3730 y FB(!)1783 3746 y Fy(U)g Fz(\()p FC(R)p Fz(\))1984 3730 y FD(U)2060 3683 y Fy(\032)2050 3755 y Fz(1)2101 3730 y FF(\()p FD(s)2185 3745 y Fz(1)2225 3730 y FD(;)17 b FB(V)8 b FD(ar)s FF(\()p FD(l)r FF(\)\))p FD(\033)2705 3674 y Fy(i)2667 3730 y FB(!)2767 3746 y Fy(U)f Fz(\()p FC(R)p Fz(\))2969 3730 y FD(:)17 b(:)g(:)0 3916 y FF(The)41 b(v)-5 b(alidit)m(y)39 b(of)h(the)g(inequalit)m(y)g FD(l)r(\033)1407 3931 y FC(r)1511 3916 y FB(\037)i FD(s)1676 3931 y Fz(1)1715 3916 y FD(\033)1770 3931 y FC(r)1874 3916 y FF(is)e(a)g(consequence)k (of)c(the)g(fact)h(that)f FB(R)h FF(is)e(quasi-)0 4036 y(decreasing.)j(Hence)27 b(there)g(is)f(no)g(in\014nite)f(innermost)h FD(U)10 b FF(\()p FB(R)p FF(\)-deriv)-5 b(ation)25 b(starting)g(from)g FD(s)3377 4051 y Fz(1)3416 4036 y FD(\033)3471 4051 y FC(r)3534 4036 y FF(.)42 b(Since)0 4180 y FD(x\033)110 4195 y FC(r)248 4123 y Fy(i)32 b FC(\003)228 4180 y FB(!)316 4195 y Fy(U)7 b Fz(\()p FC(R)p Fz(\))531 4180 y FD(x\033)45 b FF(for)40 b(ev)m(ery)j FD(x)f FB(2)f(V)8 b FD(ar)s FF(\()p FD(l)r FF(\))41 b(and)g FB(V)8 b FD(ar)s FF(\()p FD(s)2077 4195 y Fz(1)2116 4180 y FF(\))42 b FB(\022)f(V)8 b FD(ar)s FF(\()p FD(l)r FF(\),)43 b(it)d(follo)m(ws)f FD(s)3138 4195 y Fz(1)3178 4180 y FD(\033)3233 4195 y FC(r)3370 4123 y Fy(i)32 b FC(\003)3350 4180 y FB(!)3438 4195 y Fy(U)7 b Fz(\()p FC(R)p Fz(\))3653 4180 y FD(s)3699 4195 y Fz(1)3739 4180 y FD(\033)t FF(.)0 4300 y(Therefore,)33 b(ev)m(ery)f(in\014nite)e(innermost)h FD(U)10 b FF(\()p FB(R)p FF(\)-deriv)-5 b(ation)30 b(starting)g(from)f FD(s)2869 4315 y Fz(1)2909 4300 y FD(\033)35 b FF(m)m(ust)c(b)s(e)g (\014nite.)43 b(The)0 4420 y(deriv)-5 b(ation)31 b FD(D)k FF(th)m(us)f(lo)s(oks)e(lik)m(e)1186 4384 y Fz(4)338 4606 y FD(s)27 b FF(=)h FD(l)r(\033)601 4621 y FC(r)725 4549 y Fy(i)k FC(\003)704 4606 y FB(!)793 4621 y Fy(U)7 b Fz(\()p FC(R)p Fz(\))995 4606 y FD(l)r(\033)1150 4549 y Fy(i)1113 4606 y FB(!)1212 4621 y Fy(U)g Fz(\()p FC(R)p Fz(\))1414 4606 y FD(U)1490 4559 y Fy(\032)1480 4630 y Fz(1)1531 4606 y FF(\()p FD(s)1615 4621 y Fz(1)1654 4606 y FD(;)17 b FB(V)8 b FD(ar)s FF(\()p FD(l)r FF(\)\))p FD(\033)2129 4549 y Fy(i)33 b FC(\003)2109 4606 y FB(!)2198 4621 y Fy(U)7 b Fz(\()p FC(R)p Fz(\))2399 4606 y FD(U)2475 4559 y Fy(\032)2465 4630 y Fz(1)2516 4606 y FF(\()p FD(t)2589 4621 y Fz(1)2629 4606 y FD(;)17 b FB(V)8 b FD(ar)s FF(\()p FD(l)r FF(\)\))p FD(\033)3109 4549 y Fy(i)3072 4606 y FB(!)3171 4621 y Fy(U)f Fz(\()p FC(R)p Fz(\))3373 4606 y FD(:)17 b(:)g(:)0 4822 y FF(No)m(w)44 b FD(s)279 4837 y Fz(1)318 4822 y FD(\033)373 4837 y FC(r)515 4765 y Fy(i)32 b FC(\003)495 4822 y FB(!)583 4837 y Fy(U)7 b Fz(\()p FC(R)p Fz(\))803 4822 y FD(s)849 4837 y Fz(1)888 4822 y FD(\033)1026 4765 y Fy(i)32 b FC(\003)1006 4822 y FB(!)1094 4837 y Fy(U)7 b Fz(\()p FC(R)p Fz(\))1314 4822 y FD(t)1349 4837 y Fz(1)1389 4822 y FD(\033)47 b FF(yields)c FD(s)1822 4837 y Fz(1)1861 4822 y FD(\033)1916 4837 y FC(r)2025 4822 y FB(!)2125 4785 y FC(\003)2125 4847 y(R)2235 4822 y FD(t)2270 4837 y Fz(1)2310 4822 y FD(\033)2365 4837 y FC(r)2506 4765 y Fy(i)33 b FC(\003)2486 4822 y FB(!)2575 4837 y Fy(U)7 b Fz(\()p FC(R)p Fz(\))2794 4822 y FD(t)2829 4837 y Fz(1)2869 4822 y FD(\033)47 b FF(b)m(y)d(Lemma)e(4.10.)75 b(It)0 4942 y(follo)m(ws)33 b FD(l)r(\033)408 4957 y FC(r)501 4942 y FB(\037)e FD(s)655 4957 y Fz(2)694 4942 y FD(\033)749 4957 y FC(r)847 4942 y FF(b)s(ecause)k FB(R)f FF(is)g(quasi-decreasing)g(w.r.t.)g FB(\037)h FF(and)f(w)m(e)h(ma)m(y)e(con)m(tin)m(ue)i(with)f(the)0 5062 y(ab)s(o)m(v)m(e)f(reasoning.)43 b(All)31 b(in)h(all,)f FD(D)k FF(m)m(ust)e(ha)m(v)m(e)g(the)g(form)287 5265 y FD(l)r(\033)373 5280 y FC(r)497 5209 y Fy(i)f Fz(+)486 5265 y FB(!)585 5281 y Fy(U)7 b Fz(\()p FC(R)p Fz(\))786 5265 y FD(U)862 5218 y Fy(\032)852 5290 y Fz(1)903 5265 y FF(\()p FD(s)987 5280 y Fz(1)1027 5265 y FD(;)17 b FB(V)8 b FD(ar)s FF(\()p FD(l)r FF(\)\))p FD(\033)1502 5209 y Fy(i)32 b FC(\003)1482 5265 y FB(!)1570 5281 y Fy(U)7 b Fz(\()p FC(R)p Fz(\))1772 5265 y FD(U)1848 5218 y Fy(\032)1838 5297 y FC(j)p Fy(\032)p FC(j)1918 5265 y FF(\()p FD(t)1991 5281 y FC(j)p Fy(\032)p FC(j)2070 5265 y FD(;)17 b FB(V)8 b FD(ar)s FF(\()p FD(l)r FF(\))p FD(;)17 b(:)g(:)g(:)f FF(\))p FD(\033)2725 5209 y Fy(i)2688 5265 y FB(!)2787 5281 y Fy(U)7 b Fz(\()p FC(R)p Fz(\))2989 5265 y FD(r)s(\033)3160 5209 y Fy(i)3122 5265 y FB(!)3222 5281 y Fy(U)g Fz(\()p FC(R)p Fz(\))3424 5265 y FD(:)17 b(:)g(:)p 0 5372 1530 4 v 112 5433 a Fr(4)149 5463 y Fq(According)27 b(to)g(the)h(remark)f(after)g(De\014nition)h(2.4,)f(w)n (e)g(ma)n(y)g(assume)g(that)h Fo(\033)j Fq(instan)n(tiates)c(ev)n(ery)f (v)-5 b(ariable)27 b(in)h Fo(\032)p Fq(.)1864 5712 y FF(19)p eop %%Page: 20 20 20 19 bop 0 418 a FF(Hence)35 b FD(l)r(\033)377 433 y FC(r)470 418 y FB(!)570 433 y FC(R)663 418 y FD(r)s(\033)765 433 y FC(r)890 361 y Fy(i)d FC(\003)869 418 y FB(!)958 433 y Fy(U)7 b Fz(\()p FC(R)p Fz(\))1161 418 y FD(r)s(\033)37 b FF(according)c(to)g(Lemma)f(4.10)h(\(note)h(that)f FD(\033)2939 433 y 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