From a8e51b7738a5268fe8f0702b6f4c92fdf8b7a97e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Petr=20Veli=C4=8Dka?= <petrvelicka@tuta.io> Date: Fri, 14 Mar 2025 20:49:46 +0100 Subject: [PATCH] oprava dukazu vety 4.4 --- skripta.pdf | Bin 110236 -> 110339 bytes zavislost-na-podmince.tex | 10 +++++----- 2 files changed, 5 insertions(+), 5 deletions(-) diff --git a/skripta.pdf b/skripta.pdf index 69ed26b6741e0f9e6cf12f9091ffd528de37065a..583b2fb89a154d511fe465b88379a545b4c30b1a 100644 GIT binary patch delta 15252 zcmai*LvW{Uu(v0+?Mx<4{;_S_HYe7ElV@Vvwr$(CZQIFY^1X|1an9;g-HTq_)tj#B z{`J+}nOo2S+t9Toe*jiaW&r_s7guL<V>@_{^(%et7`-+(-<g`yNm(7#@I5anFWOI| zRXp;$2#l^M%0KP8=0elBwd{ZRzXVPkJIEP5ZO-N!C1Rli%B%N}ypnHhE4K{YO-Akn z>l&ObgDkWET@eF=Gyej=fR>M|jIEx39ZI}^;mJ?8G7gX-8-U%!tt;VuUZkHd$7df9 zC-?j(GS2onTq}=)-6<%KYo7)IBiQ3E_Jk+5(FQkw$3xCyhn1JR9Q-V@WK7rj$ZCa8 zYfADv*S4(tu1fje&gz_$Y-u}E0bh3?c6?FC;h+}_Jkb(u=gTyRXp6_s?BG3#Le9lt z4aipLkup$~6u@^}(pWJ33jg@~Z^o}Zk4d`$s=OPn;rjd{O9C%Ay2Ip=Uv-k_L&b_^ z>K@}oUEIT(pGw32ch`;+f$|v-F?+`ze5yxoYXlQ6inAQ5;S;WM?hb9S1KW;V4&;g3 z^JO<l$CEb3zr4Svazaxj;g`13w8HJ9zK~ziR?Bg_XaURkW%L}uB|gE6ESct+k%>=c znPv)FmJharcX!*jq8<wH+SD4ec{X{c1Q}jHc%z(U-jSn2)KC@%nZsC5C%zp)d^Xc? z(N)*SRE4r)FB=SlYQ~K-!G<e&YIFa%^S5%sKNssXmg)izU(->1(fd`-qt;8zG|>Ij zu<~E=>43~O+tQ@$6-z)@^1+&QFyc8FO8fa;&Is!urIf(+JKi%Sy)e%l;%`{Jkdv<4 zh_S!)2se?_A_aW=G8t2<P{EM&>H-lRdu6o8l?*U<3$;InA|>O}*L`>|C0RjL82W-+ zG)K|TQj`XCIP3S?z^;>l+k}JR6_ijMs{V=CAfU3UedAdE(o$n^g_YW|^LN8h#G3*M zf~w8FXn?FX9j&%X^WSksOah^@<^oz+0Trg)IAOk3XumbR7dwOxy4T)@Tpx2lR;c`$ zQEDB$&(8-E(SHrE%h>r@w?x(sDNVZ%Z_`jia}D|$RmL$a5YWa1sn;~{8?6Dci9gEO z_kbPteEnGT(R}V^gNoCUl2R{eYo(hQ#ZTA^%hSO}(M!QU*tyIhRMhmA8UZdDk{(dp z3aj)lkBAJS+#Z}3EXHYS(3dWQQYB|uq(Vwfk*`*4?WQvOJ=sKdHBd=2c888w+1BLP zr=G%%Fl0)g4?IY)x_;7SduNt?vyfV;N8nxC)oaD0dJ*1~R@O|OTAY-1wJ_-P2A*9a z9t1+Vvh7b;q=n781;z0^MMlWvKuRdbrCCAtPk<!ylTqW$j0d431StN(JyDP1*f7!C z)Goyr4%(@#<52%or^`NGsiW3hhCN;DeJWLvJrLj?#UL70<toP`t&#)9&5csJ020-G zzKt=V&C)^@VhMx3k3PF7oD$~g+&{*h0C989qMjruDj$jw;(T`e83ZzC<oW@T_YIK9 zGEXC?GW>2KAM5;&X6;EYo?XZZagMAr<M+%%he3_lKpg!1VaO!(puP3effafY^FGWt zRCA6jn~}l6Sd4Mj-fXj)lPM*BVC9l++YVA^+i?Y7v<0%9I`JqtyF}O_O4}YbFW?$} z#8#@Mtk6_VpvdYFrVe%U8-Wx{%b&u=Xq2@eC4sHnkixNND^I2nAqUdhc<>|z_h~Ss zx*3fh&GaB#h1os?q9I~;M+NeJt&FFUgO56Jr&gR!RZ>Cu=+#^<Ej)-pVAkov9|xg1 zMw!Ruy;lVwb@`Z>^nZQiwh;a$3-v(CkMkFnOosnF3lgWP`md6c#uN`7qbez9$jDjY z9No{1xfL<{ymY8Nc$0tSm=1^KTp144^#=+Jj{TA8e$La;X>+c;lWm;Mt?=9=?r?H4 z-&ROcD7j7p<J}CskFA#p0O;@eqA>982K$IzR#i1SJ!{Ay*a$PfRni7<!W*o&05lM# z!VjRf(ggm_?evA65Qoxej_Y0DtlUIXe2le0L)p=#5#zVzZBsyO!IHNw_q22so~B;R z+LDih7&?(~AO)I<KFfQgK6hKgC^dhf#!zNNL8$m(-fn5u#+c(IFe9H#!v+OI_>%SQ zY<UdNeY|hImR<dpJd!Zb5{E;YHOHY@xOYElHY39>O;skeNuCi&v~X9$QMFrg=;+5_ z<gXz%@S@m;TJ<0gaV%>o0y!O;0EP33;?o$h_QbtED<gG;L;0-3Fn!z*$QpLuxLj*1 z>V=c-opo5G)qK$N0BH}T7mC+d>9R(|&Iu9xRVZQ%%E2p&KUmpo$%{)?#W%|Jq3`^- zcJ{W35cseZ(UgW!5N7Ega`_M6(kwM#wL<Osv9M3fG`HIsT*m{o1{HHVXot~!xFS%j zE<GgE=hwM*xVOKaf7Z0Nb&!NKIz~iIiv%e842)trr|E&o0#F)TvLpdfV7_SfD9eVh zPZsg&Xayi6P=`&J%1y{LMj-Fz$$!c9;c!#B<4l(N?Idkuu#KiFOLmlG<hS?mZ&cfs zLel^pLc0+#mQ$-WKhXOP+3YKn$L@O2rziL?T6`Y0!HswujOk)UOSCv+t<_wagQG^@ zY{zu8e$ag(fOb3gr!^&(uZ!UXeN;G>qFLj|L}^qC$49shWZ6)D-PTwvV^+<(QD_{K z<3DdfA@>MRZ-?F5)Hum}bP`qJ@rDJ6GIX=yG?;YlgDtmzuL>XE)n*~`=JIgicT+3D zzMf^)Juodyl;Qa-Ze-L>pFF#w6~}dy)#fSUHfu*p0E|Dh-%_%_3&`Tz#W;LGly^*2 zM~>Q$1V#*SYu@KU+U<AJ^5e!<-yX6H9k?8^Q$Nu8GB)9Ps)t}QdC@A@JX$xvlo<~v z+1~{fIz+2qo|Pe1>{G1|9YII7zp4x>tIBH2^Wuw5V3OHW85yB8;qo#}=i7=>2*tPt z{yj5p0$5cndZV+b?`g_01$6aRACc&>Wo%Qho1NvFw@I9NWRH*|P);W^*~KKRRJB14 z#k@4F2vvpcG0~AZ7I}o<6YUVo8(kYa3$n84iR$U2M;K<xO$A3BzlK&ucS@L89ydo{ z?TaJub-7dh$2Ii6wkKIM0-4NTzL@(6HnmXY0S_zu)#EXllW-^TLk?J2i84qNSqnco zhMn2#dAZoz$03HDx{*PqD4z?#B-t-AS^>rzne;T)1?IjimKo;dp)i_5D@DHM#PhVp zV<u<lNtvRD?cai#Tu02>pAoQsawxTR=SEPeZU+L>+O$N%-P$cs96E6*WG~$tgd!Ie zfL{@5cT~CDvn5Bk4MY0*5|w_s%b{+27S`M{sj)D#Cv%0NpnU=-Y9;p?u_N%o9=#B{ z(N`4c_}U**hZzQktDGxBXPERHv89TcH7h*G!U&T#HrOS|q>^Evnb3*m)kRh^R|)~T z5h;Vcf%@=$Y&dW1{=@QbDaMVGEatgF!1+ufa9gF~)%OW&KP0vnhWfla1s6G#GeGo^ zK_3=U*0^L@TZq=XHKm1~2XZdrjDI9aXYH*re62@qP5xfN7SHdu8~BBD!Vu@5tOPMV z#FLpXZ&@~35PS5naxh0oPNGX^A|o%ZHJr?uiP_}WnW&_UwvDC<O|dQZ=Y|y;D8Zb& z^Q3`P=ssNiTCw#TbuZW5P0YUS%?u7MOu0M~c-oS-^fC0i_enW0NE?-Ger3^sZdB<G zM53%kr-%;lPbq;j-##VdtR6#Z?)uXFU;u+2bK_`rBGd>Qn?2EVw&7$g0*OvLx8=kn zq<NCNG@Xr01`ky$6+a17DN-r|yxdUp2dJPtg-(W6;_JxDqXMoYcV(+;VGR+Co{8KY zo1<zIgLM_EhaN6=Fn5yTdYsIV?W46lo3fyu&@=%BN)(|d2cHe|=_Ks)#FvV#nhZSX znN*LBxsX$2kBK7U8$NK2fvwZttG~TpiQekY!J)VMMJ_Xp1fpFM2JDUiTC;d;qm`^R z<6UL^2uL80gh2*Mh&LzRt@U@Y^O+_B>@y`iTXjdXgs4ob{Y!4H6C<9;`|e!!>hdNz zJHd{5lbpAuaq>6gRve3la&($)mpX>>$O79-8qc0edLPFE&=NS($o3_g-D0<NROmuw z%UjvZW%z0Vm)3{^7$Yuljb%3NnHj{Eh^ofmqF^2bN5e^naXl%s)LI{9CT^Q&6Jgth z0pTBkt?r8*R#JFNNe0jG(>znV!;@GxTF=QPgwPR=k79b%DlppSr|Gc)lUz+rS(l-| zbJG{cBq`SSpvYs`st1pA<20<cnRe|c8+)v^M~Z?Yl!V>iqu+FZ){q@%CvzJ`Oq3G4 zkg^ON-Pnz%fhd&=6_?HyiK?ypn+#RrbZ(gn9yFl~&`YiW?|tqP^?mM>d0fb*a&x~3 zy@({X^dN=Ih_T6Bp)|<DqX-UZEJWpWP6xFGGlu$irPxn`*5iH|>J=|-kNm-qs6n*o z5SyqouzSu!Vr3WL1(sTW{Opx2d#Xl?klE|}yY<2pX2NnJUoqR>fJZ`<*|@AZM4-5V zHRs!l!!KaV7{a#F9gu{iI7<gpcw&}OjYf=qJy4(>r)<0$`D*#d*&;EOFeA||^_nB( zL<DtOm3MYw)Ql_?HZDRL2`b!kAvw+q2JlTMmF-gtdTIhqdZfiS>G>*jzwD;<hC<Tg zs){CX$n_WhNa{`u{))y&DkCOr`7Mpf!Ei7*w5Vc7FjA#^@YGBd00Sdod)!@|O%`$X zbK)LZ-7qn|>=!QWt^S|){_M}aSYgwagO$+%1Fe_<o~XZ?500e&=m;}|526Vk(kM+` zb4Py^JSmg_;(VFd5LHfMNrkf3HzBNuA2AJAVa=;}!Te0l{H+g&-ta7Bp$nWYbdd@t z1BLsWZT(>()ZcsXM&gjdZIG&wIiiQBhguFX@;k_G>5tY30Clr+-F7(Q*#?g7{H;q_ z`G4$kPEXA%|IS3&s!Bc>a-~1W5Q*4+<W)qfKt#&}O3cDzGF+ARif8jPO8N<gZmge( zc36A$E4!0CmTgI}DH>qr$1QN1v|(h+p^8VE?NXGR&9F!K;QXw%8L;R2gI&(@EM|!L zW0r5<4oP%Xr;B+M<5$1`=-c2JupUD4Ppb{Qx|AHto0b?Az;s}o?1)ed#A}xL70O#! zBO9*-NNw{7Vsk6ZF8KR36)Bv2C>8}|6I8PPl*aSrmzIr#9&DQ4pU!M-jZr!oDVds) z@XF60|7*|AE9ql4PJKe1Ix{d;nORG<HF>1~DBB;qO)mamtfr97+UwLKW9nWtF>oui zUZ>c7a&pFkV2~R_7#9#wC6=J4i6a|?qbzO#_OazQ>09sNJdM`1a9_)JqR6(@Rjgvi znFnk}pYT(a_O`*oI>?ID8Am=jVIUIzlAS0}nYV;^xp>}1(7Q1h-)3cqqZ7IGC-tAy zg#5*$pvZO^U7!!&kM`xiEZK^Xot!XS@%?@D70C45KW8T;A`<s`Z?Xn7xuGCt##<f( zKO<2Nxb35mR{9yoxDO(nMWXz;PqH)1kF*b8k}L4kzlR#s+t1{eAX!Exa6WYN2PkFV zco1TY!<P+UtMp*J{z=5R4b2SsV@DLwN)GGm=d+p{<<Lz;fT^N8%)jEQlkCURtS8^} zJC5o*97@tyzC|3}RU66TH~$XOIa0_&U;txJAj~nUx%up8PsmYzBdWL0=-tRsd!}O; z$s$9KN03C@{!E$P2lR7o;7h{;89C}72fbj~m?E>rM#j8lOuKK{ziDa82z*Q%Ky)ZK zp0vaeoGrI;3TFzY6)?p{;dAjI>iaI^>Sm%w11MBgFdd>U5Y$6w_a%J`uD<jlP<g0E zq;nE4uOY8G>#0{QJfZ%Pg=Y4?zF$HcARTi_nV<33+I6zoy{?fXqkfMC`%uB|?3k8@ zB_PpelcYJDGn1i#!g^KEVVD_raWlG;zci(KWs~uufqC806F*=tQzOO1CtDzcaVx+5 zbo4I{REFZiVpv8AZQ^qX-u;3RAVc;N;^ZE$d|!86*4ooQ4xVz~Pgg0RkbhBEvxlW| ztad&Sq8;6gp7>8ibcH7IC!Gv<Vt(a6=^@_kmEu-^Lv$H=SpRDGq8zX{8Ppzf;Zs8j z;mXR5bW-fRwj_<m{+7+G>1ds6+2`L`T<#jk{zMl7Rm7=PTgrb>b=WaEfI2smW^wA) z>aD%1s)iMj?B7caP1qsq;2<mBUmV?4gVPVPZ7ItynT*AMDAO36YI#sG1<#`J;4g<A zs#}R7dTI2v-|PQ0DEd45N2sQRc#?Inl;u!~`^fOBeqO3XcFx{Kn2V;6K%6_PrLlG| zc5ac2W9jNze)J!41g>cI0DgM*WnOo)8za&_OlGb67@!K5;&&2yEs-3%d4{5{HqYk@ zc<YX%;SmQ5HE0<SH~(i<OLU7hX7oyMiJn4L*K08=u^mw7|BwjY#wo#q%t3+qr6boj zGeGo3)Bj=^ta?l5=*hhcE~h<CRplou*D6_OAxcZlRMEL1SEDHcuuP!^<%Z5?<H@dV z2=0#@60#jG>kCxRUvzu~l`9}pq=qKOGElMNBv%K)w5yD)H9xi{rL}VWIUk--s(w=P zG4vL%44_T%(N8?N?$b=c$dOAU7xo_8^25e;WV{SJl&7WC`59~BMsNIx0cFyruJuy) z%$IY|iyr|V<J<29#Ds(pATbz{kN_O$E9cGGEre(cZzq~F8FlE8#mY_Xy8bvmDtF&K z;P76tPNO?88@``0W{e*=AMXt-F8GN`x0#6<Kv_&r{Y89W>FhG&+ALSQb`?p@Ei&-# zXkkzjCKfucvVUO0a2%(3=|VlO7Y<|+3;Imp?FLP&<Wn32y-a&2-=m+zJ@P%4Qa)&e zG)9UaP$JY)R6$LViceN;kz9r88Yyo>IVHOb<V}C=#KBogMk(o`hC*dbK{%gb<;g5l z2i6q$&#scq`QS@^zxmsK6?T^_W*Q==Unr`*1*P2obxAPgPRE_Dn1R|_X>5NFQanO< z{4gdXDSRmhx{8`2T#FJ?#e(je@f#@M$IOm|sPS9UwTTXBLR8}jYH+zCetCSQT95x6 z4mtp(BT}eJbc)?yJq9A`w^c3Cd}CZX(<K&Bj`qv=Dx7#Y_Khydxuh#g&d+APP6(Z? zRJB~<rFBS~3(rj~`7r2JYWp#+LJLPW)#k&;=&r}Z0v3%rK8BmrldzEU3}I7hfV?K$ z$S&#aM~Vm<iG@8Z3mn7Yp}dKip}!pg-T~V~BC7=1Bwm2^e?e2-tr$XXG~lG>v}I$d zEULmb#f}B<J8EX22lpt!p5Ns*sW{}>Xjc5kP1(Jqd&dYrNrpa$m~>-$8gYkhN`>ze z_dpB;V*1y>uG1~5dLl5e#q0a5`0vC1b*o};1%SkTr4y+is2C8+<%2p1iHqF<v{?o! zK6<VipN$3a3EsB0x|X5eZgQI-qKw~%yXSaL|NeCRdeH>X-<$Isu(TCB`4YN3tNON* zjT;HE6I+r^@Sg9RCE*+I!Pt|91>NAdvHD;PhkZK4rBp+Ww=tKTkQ^%E*MsY61Q@ng z0#q?I78SESjnbqYHMQde5p0S9?#brC!f~GUf*p$BV(#hWH}XYuwN-Q4u=NZ!e9tWr zOA{|V8rMMRJH-A@(TF4sow;MG1qJJO${I2pI$K;}T?=sQ2?t^ElU_xU?=GI%%;HRe z@s*mt)=XQ(i+=d)?&uEK6zG}VWq4eP=m&u#$nUHCCZo!ufSFh2!?afcj(xW2faHxd zi80u{sLPdyKLcAnhG!j<4b`iuxv0IGV1KK<QEU8}zfA;~6?>@&{LKGRypJ+99K)Ep z$>1=#_8I!tJdxp5rcJ77FDM2Dsa3O=aeb}L-W!)@E+8wLLy|lq0f0EqJ&`~DbU34Z z&v|y#%3e>Fee$|7lR)nT*l?!OQLG8CyhBm5_O+|G*Do>{C~>hm+5eF@v$1$R<jaoG zMhNtVBcJ=JJyNdLlC$~O&!xu>pM$(GJq;(~80{rV+uv5H7&Jq7TS^zW&ubhw?dScR zEZWEZ<Gn)DWLBT-lfFH5>}1S_DXbsAb4ZeAOPD`W1nx=^bN#4*<EE@gQFeShRYabn z?}Vb^)XKx}e8QFfRnH^4_F?<?Ta_kwzVjX(Vp?efuZcnui%D1v1<s`=y9BI}<9V$1 zxM=a>!LHja`pppsd!S0cvOQvES-$id8J{Ynx8w*O$i{?&f{%|W2a->b?G#oAYFgYl z2oeDo`KJvSA8%eD|7B9M@t(nUlot|<RIc-b_SUenS1{iE!=J&diizL3ivP7))>7;s z$sPBMTYho{;hzZm_1Aiek1N8H(~qTo@6Z_gJYv;qV!MNs(IqO<Y<1>u?+KwR*_Y_4 zAA|~Dxi%l>rUzEv*Dc$dwH>@BqNV(bQX}K!V#1-jWHD}l=0AhqQeTbqdt}zuM<dz2 z$A|PiNO0<%#0HV}ppqd<0=yN@y5J|iN{(;ljy}txy-dzX&Qn_r)&qCnl8*Q*26HZ? zRw7+H>kEFsS&!whh#9RopJ~`9P(`h_1tjCrh~?KFXH7ZUI!fE9DI;$?+jrUSR=5wC z9Bx!c=E9o+Ypu};#hDPP`9e=hDE?T$bv~o=1eFk0PZVuR+5{wDje}8;P*vm4Zk&sQ z5~kaVVjt{u=e8@YEqiuioKhGX_+XUP&1*L+Uvi!AS}%#^Z}}N=#BaFclFrR;^3Gs2 ziOVwTFJhjcqCmyu<@*wq;6u$x@d-7~YIfSRGou{fCx=0bn^jCxptfvEnQgm*T1vfs z+0$Z4jt-8fnJ59#>{!2+TA$phQ!&HvzMTljOJ9@n??A=gh;Z6y_I!w+VIov`Jld1+ zorgxU`<1CuVc5{Q;ecVtjiw76tUNJh;{)H)&k2Ka<HWR_>`XjNo0j0G#di;WP3X7L z4_kM`O+I_~O>5~`5gM5OdI1NhEGc^$!H-WXVa+u72EM|MVfs8WW^5x(a%Dz@3s18o zIp1LkP5?RVXAvW-*{`HCIZcW1VYT-Oa1T4U(Fa8=_2i~479Go~TX8zE)_Z}3opd5# z+$X+r>>=9JrP~#}{U+s$n~4W`R39f5Nj96+wf{UGK3dq7yLJcEf4h5_u$Y^?RF^TJ zu@f3Kr+;7z(4S@I%-h^=y-$IxJl=M<lzZXqjxYz*xItam!i<6W;aq}(onxP<%l(n! zf8pGl<SmtPa&!pt)mATR*Bx2TB&`MX;*_cEF)CG|vod(SjztIRBu_KO0qwQJW&~YV z&a;91RVzEYlhKb<o)|O5pkchIvunbp_`cP(Hy!+k<%HG@5<uUYs+>bfVB;fFT-Sxk zUDXW1u<~W|#~crnpB<RO{@3YScg6jBipLs_mRFi;>TijL1&klV3O)Y%8^)Y#=ki$g zg>MgB-kQT*`}*&WKAArhxpGQ+5V#s5<`Gh$9InKUOKhmn0|W!C5jdkHJD{qM+Hk<J zGnlvQ9>%5|uz*M!xle-zX}WL~J?)DpbY*_Mx{D{hPMxF&uM>4VI<;eVJ)Rjh-YoQ= zl19$D$Zc&h_MoWptx)}tRDHGpi}PVVTet8!oR-toiRvl5>?GCm1>#0in@I_>%m!xL z18rc<_P_~dG9UmAOxnqpGKUaXx-x7;pF^RgE9Z>T2AIW6Mz%V~N}{sb-&CUWmh+P< z)!;kTt}i#kZeiZCbQ6^SnN`6;&pC0QGQ$k!L(m5ytwt7&%lm`6uiWvurA2<$IKZ6B zfVN_~z)W~`md>*1=#B`2)|<LBT35h;=dR-KfImF*uUM42N^bN`pHl>^4O~oc3GIQ* zY9rN7$OQE)MxZE1**Mptu4s7V^+n<^Y}8x79k&Co!K;3F=X9R5_y=pe%K1yH=%rGo z=o{~&w>x+FD9$IGXA(l?7~!XdGRr5n8{%JFrbS{mo=YS-cqJpw;#Z}7W@E+F(1+?e zFuZ6$dSp$sX^ibMYf|x>_iSh}N}RGaL;{A-YCQI%6L1gXSb@Xu+^CE9_d_7SrrC%F zG>cQI>~A?ts}d=HT*wOp_WC-?=|6`#a@+*HIch>lXhxb|FHiISR;zx4CK)(w9iI8Q z7hd14WR51js4Fk+7ZSmJn+l#cue?1oNakQ5M}R>06#!-XdjU!=W}MZH4*lF5hja`( zS=Bt!7O?X50%yb#BU5bbTO~H&a37T+dR6ibOTqCfVfWawLI#62k%*b;d@98H)4OtH zZJ#0Uo1OL9bV#$!$d^QpHRj^{#);=rPw6S=K#6BeaGdyJ!YO&C8VJiS-;Wwc8gNw~ zp#Rjwp%P__UeHi6Y2+PlFwrS~{z0(xF#Rtuo9XZBwW1T(<2U2I2R66bG!|WBgbgl- z>|BV~2u$Z#oyoRV4){kkt545^a(;rk*TV#coF4#N=lr4FD}0rvw7yF}`ac|{dc1$< zisSU*mi9h=>+$aUw{%hKu-sXi5+P@nKLp)hdL8h3`gwLIqpOX95EHKPawlrN|3+V2 zpQ|?iq|;;tV`s4jSKbB@&&Q^Iv8PVu{9M&aKxgr-MpGlHceB-G|D?`G5P+$tpP6fZ zZ=VKaErRqhMW2E#ctw`0%-0@|l4H*QxHiFkon6@OZV2nWy^wUEUtp4C`&n||-?3cJ zEQEOY&&n*V^aRbHR(1q$&jcBf)N%7!)Z7}!enwi4qVOf#`!>W$#2c;!51|OIP2>TE z=c*`>63xD6CxzWt9}L&J^08A+dP^IGXc|IYQ_}Tt36vvM<i_YKi9Vibj33TilF8OF z_v1R(roQrX$BBQeRn_n5v`_~)WqhM>m{jrMQrO#XfG0y?n)IFo(n8FJf?SzvfaQNG z)hWFVX9CIi-#h;)RV-7H({@8j!tlJ(xS=>RYqtgvA_-}}^mjyX!f%Zfz-PAV(zo_L zXep_~YA8Q_{glee$pmffrKQ+%)F8H?#p>8<B>`+5ob?EBJW4V=gb?r_5xK6$YG_d) zM0{8r_y7r(U3?*+mw@eC)hRrkuv~Eexri5PT`5Tss1lSoJ1VI-|K1-gQbr12f?(cB zM>tM|&+ELezUPxC(g@W)FY?~+#|sxdn(bUKgjE$lGuzahdjQg233>@a9>)~+|H6$B znw}$8kCOQ4{hs^#HmGhCv5tv2sbCN_kY=_B3l%C|2aXaTx6*M8g-l(>C&R!EQpP^e z#7!1LE;P&P9ZeDfFQf>sf~ir-qvnE#6GszCT*p+v#T3R@P|23SQP9TR8$J`N${iI_ zLvNerS?r5)!DS0XSgVZ|Rfc3lCv#<P1)qNw@pB8ID;JNUV=<-X!;3dsQhi3R^a_iU z%_Eh98fFHZbF@&g!-ObAmvvMotcqy9mCo9P29tNjSwT^FL0lJ!n?qnpNy@`EgR^4) zNEAwKi4_ymME;a!dsJWr^Fp4KEgk8Q^7GHuJeBd!hEayw?u<#KPsa#GHzer|4~+kv zTRBHmp34&YF7*w3L_p+0WrGa%Q8W^!PuNPx@0|ij2KS6p5|4%3Y6Vw7M}!<=E)_ad z%_yyiN4G|ZQ<5a}149b<MIKPiRtPf2``$Nz>W0Z_`vW(8BcD#zDL^_BjO9-nWWQ3s z0(g}?52clQZQyRGkdNrMpX6My%=NG`7J}#+80;Q#|7pxYK8D$jN2%FL(se6RuQNZG z3vCQQo)9|FSW*&OiB4pJ2||yCEL90{5M%}Ik17&|mR~3mNILynCeK|&6_qYN7V{DI z6u%Wbw-7}RiZ=3>7!DdNGlb(Iq&~_MIej9g7D96{J=r{5JF1EsE@Oo^55~HoGwozp zZ-(5cawQ(dHkp1DdF83tDC|G#!cu8}F=>3DINDX5zA4U=-YqtZED@6w1*WLfTS{J- zP)XoVX{l?WQVi|f<L_{;734>C7RPr+@h2-0P3>k<Laa9q=pSmeglT_coEtx2g*Fa_ zKwD&B;8p0@>F7mQU@zesrbM@rGpKW-g+oxz;!M=k5vR3dlcA($bnW;!9*oqA;4J6> z3L#rp%*rWdGK`ZjoLI?AZw?vsZ}J9z{5(vyrXgc=&OeRR)Oow#6AGJ!92BI!6;}pj zvmKVN3bV}$4&my{Fo};;l>QJ7qp+jlB8B~iqv9^-*$eeYolK}FT<crvH@8Gl-ojqY zPM<i}3$CU@Yf49ff_uoHpSPlK*B9pM0I>q)g819>`GUVYqeQ~a_{hRqZTb_`v8a=Z z0A0+)k4+&|s-y4eU7(#F?&FufAtN>exi4RBkVTK?0icJ7ZE5&*nf1@}_Eh<;m`DF{ zuhsj}Mo1-wGO(=rgq#TN;b5#l^2;s6#|M8BI{^60ks2kLusyV<ee?K}<=jjXXgBar ze(sV&EuV!rxA~Q=K!soc%ca~&lVc(<2DfUaFgw8l)n8+|u+XxUZ`kd7-{_<HTRU+C zC*a|n+K~8U;*K*??Kp#Po}}ca_$UEp38;pSm~)*^;BUiEB70%7p;Mnx9o2a;%kA-> zjp|;hF1oaSrKrMsl5TurqeQj?^ia-_{N{Je-}>GYOB2#15)y(f5)zV+;}fDS;uEru z;}ZNV;u7MHW8+E7ZQ4o8&9fi_*!72QOBGl|-Y2Nh><dr855zVOGK=%%xV{alid}Y{ zE8(7^?in$irn!h;(gX)F=i9hR>N5&xE@->?W!pjU3nA$1xbhE=%H&A`k$R7v%^Ab3 z5^|yq@`J7eg?`lvscepo;9>-np|4M0FmlW2E;caOJ~4NQlx@Vtz%(ZRNUL_=zrR}- z<D5$Vyup7po-t1Zti7O_3*4GRxIH_X(`j`simXd*>NwRKmxccGyTnP@JFoqhebXsW zaS+l*^isP5qn%yTQDgwfziF_9*s`kpR*Dfaia<xXisO1{I<w)?;}UxVH^!ddJ6Wz` zWsw9Wb<?CPmWWGJAmM=wtpjbK%4{-!YwW!9RzhH9^NsUUVqm0Fc_XzsJwYMFbPcC` z$3$Cx7++MEr*U~TW5GN?zcsl>A-BNpl7h>${SRT5AAjF8*)am(T@zdct^{h^$wOtF zzgr~^aIoRqy6uX_3ys#ITj)j9D8Scu1{pKO@wmjOMuoSBp#Hf)3dM^>g*|J{RZ4~3 z*H>g`S{aVDn?c{4$Oi4}B7WL?Z<E<crOAp;HW1IHHkXgcBToA&uj;-fT*nqJ%(ow` z*(2De+l8dO*~kIEDWAbXn0+?4(FlJHYFVnpOcvdv@fxyWnZT^Zy5u$v-dReCTUrqL zps}wBylj5v=CuYl+dIEar53UFcOqc9^;XWU5Z~QSnf{00+Nm0}USDzGqU0BBjMnzs zQhVoBL$#~|2Q`Fbkm;z8t_i&_%p)~2lUwyEQ1M;vD!hQ;j%Fc2@V*X?*5zDguAJr+ zyfY_-Mr$mZrqeW=J4H^PW}{<D#wK&_rCzxa{PUXQT0~RlY7?_lC!8fC{iDQ5jINZH zh%S4UMv#4;u@zF;uStv#ne(Ajlg88+627!-0iO=sNo*LDXq?Qgp+4!ih28w0NkfbJ z`Uj-v!&v}VsC6WPt7=|(SUUR@k6=4H+;7y+_i4hx+NkWRvo|EK=RYyl8swW`B+Hfd zpI{_ww%_rP*JT_qkYRjA8}czxUQ0t-syKX7owIyI>k0VzNRUoGQ(^Do@ECnel54sH z)FvuP^hBcM6?BVyDrZeluaAU|qejhT1^U{yr5ONB_TNp#J@mT=W$ak-%opB|^j93^ z?UX+`L*rR{ij9%YvImo!+H_lk3M-_Ck>Y2&;%)F}e{&@HAp9;LCe2kex2L*kT_hke zqLi0TsaacJSeUp-Ja#0NzJsYKG;rx;NLoXwbS9m)y^69>86x6O4Uh<|u6_aAvrwEX z4fX|^)<;EWble{ss`F5E2;3^N)7i~_=|=HA-*DXL8eh3TA1(hbJ1$LUe^slO$I;=; zPb%Tk_`!M4q*3t8rfSPu;!ibu_DSiZ9FP7KLt9z#rdrCTR)C_|2A_!iu-&1sy+z8V zYl6#`m|g=kNgc<Tv*%Dr)fL~Z+0k@2{wOOT-?LcRXW4AmjvK&U#m8~{aDVli!bNY# zb(E=1=z{aq8PWJh4Bt=`-)*8hi+#bsCLj@5hGt~5^WWP|kDpK%*H>RsmqQ|J0XGr+ z7`#t06uj5Ap84n}vkz*?(u*3Q(m$d!g8Si~XnF*3Q`e-IF$*!?oKi6x0Ns)-dI<1~ zCAxVwcUiQ#beAL#P3zfQ*I_2|j@R`!SKQ}n9Lc;B=S-N0x8du<UYPu#;ULPh@1TF# z!*|!3m2K+M3+SFF+NzO&xf;AWS{7+1x&$Sewjy8IR%=}cUBRuabr<N}BzA3YwHB>K z-zQsij5}C4IN<6vk6s;ttXva62!P>}fvS-j|I0gE42IN#X0jZD=MMUb^VS9D#*uuJ z5OdiW@r+Gl?e&+x(ask}I=tZ&Efc@Ahzk#YaRp<yR<18x>kbk9@`P|QUbb-SN>#*O zRygu%gMNCNtx2h{@~$IDqZ_**Qkal{<TsY&?wpP`v5%nXD9{sPZO3?}+XdPveoqQ0 zmcN-~Pj?k9ndpFGun*2d8qP1}U|nbf2bO-L=kGI9Y->uP1S$ECBnRGtt%Oz#uN?9% zJMok#qqzK(F+J8z(HxMxGJodj-miCKs-TQ;rH>GOg+o|z^{L315|&?H)c-Mqa?XaL zjzsXrp5fh4#Ix$fU*W4bG6CT81%vpIF&OEb+Kfx2UJj%kPR2Mr!?*a>gpd0=n&7w2 z*ttPRsq+Sf_v8zU92Gtk2NZ1QUfNUxnLWWn$#<z&2iBoaXI31Bm4p9Gm<*BX_|gsX z%B1g9h}@2f2sgUQju$G{ti^jv)~!uX*|D7~1iC86<gi;Mjglc|IstDs#SjQqg3nGu z+WT|!03QRdO@AMQA8ezXSB`651~D>KV`ec~A|qZQMp&;e4_?KivZ?*9NISMf-PRA5 z93c)V12v`_om#7;IhxQdq&X>ANcZ;A0*r{^o!HdQuZF7(+9#<0II`ZNrvD;qUnppw zq}7k!$r)!v46=)^r2xN}G1n2<O+FBx$bPhsHtU*=;^3``ADf!q;zhTd(m~WPzZOZJ zS~6p4H)I@s+KqK^ypcX9+hxljXf_n^niDjC|Bn}IXn|JWzl+kC_2=1S_U$BJ9&>44 zle*%Gbb>mZ22lOCb$zud#E(m1r?%#8FbgYFvhc8Fb+ymk#(*8^w|e|&=$I12dE&MN zKFn^PP%pL$=!mn+zKFh#^OXIVxqX*Ayw6FCr8O|ltPstTrOUpQy_<rGy|tl~{T&ps z|3LgMDQ92<z@nvwlKqzmEdomiA5Wg?JrDIO>I<eVMl)sUkZB6>3H|8I$|+vr-kGOz z{N>?%X~~2y9WXMo9?FUKY1n4*<_~jxr1PWjBSgXuxO?RDBv`DEw_&(GXc)RTO`sGr zo{v`hI7sxTa=Z9Atg`<{J#4LKM*c7kyxsZ0d|Oag;vS)DEJ{$}n@85X_;zu6u^k^U z!-t<(3hL6vV!{!d-K)c&9ng~ZQV&>kODCx;w+=U_10YE3U;9H7g5(W`AEq#J46aC# zs<{i=mpt5mn{88W{F}4(e)xJXa5H<&<OqA%aVQ=v_%?>W5`G-PFy+9>mk#PaO0X_% zRDA5Z{{}T)0JWJR;9F4KvmEarWV>%Hn{2bXrvF=tb)ie4t1P`3b|oKCXN9cIru$oK zWAnopv1yep!Jm!wf|Kt&UDa2rgv}*#X70X+HquRuogg#Jn8!PLQ1<~8N%9+q$rVMH z*7(+a7K1!vlIL+4Aoa&UV*MtuM7Y&PWt3o<a<qUl%0aWk5vCo=?m9NKOYFripfE@W zGNmpH3?D#1*r&`2JiM>|>T(i5rCH|eK65D=Ye?LJfpaBbE6`Q=FD7Bn8+|qj>77VT zLL0UD55ii1dd6S$7pc~ts}iXsOq2E%A{E^=3VCgmC$hL!BrDzaMcN-|w>%e6I=NK# zrgx-KQ{QmG2NR4w*6$nrxWl5yFlfwjC{$W~k^p!c;Ru^iO)QmebPl(wN;%D{-{;YY z1rnH4>*U>Iwat$8w7=iF6WJ-9s;|P_J~170yBB_AJE9sC2@iVgi|6<eh^iiYAppYk z8Diw4i>kA~y<QVBR4%NT#k6nP1&{l+RK#iIa;TQ#Vj5>WRi1@WASMRQrhM^9x#S=q zqyajSoU7e2N4F=Ts^rqS5MEh$5#DG{^%)#ktu?k%s|Bk}x%53EXoxVcoOP%K#_vhO z1QPL1OyAk7nUhoq3We+nE5^5^ifT8-Ja5A&g1nCxIKNMfWtw+s-y`iHC~)6E$RN|} z$msmn&whLDtxdKj;bTT3xj|JVi|_#F-~)E@$S-W+*>mN=K@xqLuz2a|pO2I-4Dy$f zhq9W6rh;8-Wc8b4SVz;|<5{1|*TZ4t?(>t_dv?e=Y*_H%*pzuHLXw90wbOemrfsp| zt5I^|wq|{WOMK1k;SfHxWuc^vxYULrE-Yw!o~jy8au18FC~+S`!neDOJDIYZtAH3t zI|YTV|B_Q#Oe)#|+DhtMkm$1VkqW$MsP7gnL{f>*?9U;SYjTL?;$D(7HAV!stq|XR z<!VW~q^pu&n6;&TNW!#Os=oC`+Z&lVU?d8Wn4k2WQuJ7OOTJ_79FVt2MNix;azSO? z2?B;qa(vtv8sQKyw?vS{`e_jV5`ZGDqcgb56ZAog+rDQCLRdu}@pPF+JcrOth&Wps znPiH#B@o6gs#evF=}+ObyT>vNfw2HjLWgTEa^A`}2-8|KvgqW=h$8|m)E-bW!%A4@ zB!$%RM(TM78xOI(0)%kPDXH=|h{{;P2H9vl7nj|P&EV%e^k19dq=p8Hn!t}&Waob5 zF^ZF5!qco@!w^wO4AkILO}ppBKj#Dnpg&_F`iHnwdEHXBLPOgG_V(3+5k7-Q=cSmW zSA23VF*eClTk-MPb;mUN9Q}he@X&YtVvPVebZW&J<UB-A=lb=L-LUp0=I(+6s!mHk zY7&%Vby|MkUmkz&26hZOeE`-jT)9HvwV0;|AH|~b-}8l!vOb~Wbg^~Gu@9T!WVZkp zp@N_~%n@BS459oq2_Z_wm`UTS*Pm<##*rnc7Tv)D$+8!!rN6Em?Rs*SXHcg0)O>Gk zO2UbPCGP1Pyqs6qM|*!08&QSt)?{S_6X%j0`j$dOg72*y-zxF50ASh;84&#PWYhCG zW~3okiD@HvnC;yrDeryBUqFHAElM7V=<{&(;^HRJ45H47hB<lY_q$$kf-*2bp<M8M z3efu3kpFa}%+Fz8V4Ff>!$%ZFm(5oBvhjWHr=Rgev~kU%tL!JAUijx;!+lP|!Wn8g zHG!wL(EwO#YBAAPCm{V~|L)5oauv>~a${0J0E!VL20Y%JhN9Xf8xKv@<r`CV^M}~y zOnx?UZHPqJ<chb<`ls!G2fmBlL+N(!0x4E&v^~%|_XF|lI+w&&YZ8EA<LiZ0-ABRE zYf4FoV2`0Q#x(}LJqG=rcklj|MlIwLBtm~w2yJnW%B}kipwk>$6Na@jEVDV%;F_?5 zLwm=gw)s!V^F{C`yUVlAY<TO3+BpWHO)2gZzY?4mfm$XjQt54q#5b&e3c+pOrM4J` z5VR7_xh9XqN^2s%hNX)k#kyK|AErkuKsWGpUb=TktT;08Ar!tQ7XCq8Nb0c(k2T1G zRI`7kK9BMO-2RPS)Ga1GN^CTtGw4U|bd9JD!`_gH*nt3L4ZaM^gc!p8=j-;Zp&({P zvorL=l|Eyy3Tp?e)>b@%y)F!U>XyU#MDd*$MXPzdCM@Zfhs_I|L(AL_4nz4s)8Oac z{oYsz$xfGbt&3vykUezEbBDh!&6LJUzAl)o)PI}Y??a7;I*(Z$$@XX*yCxfVRa;cu zSLEHC8jtLiVon$s_3HdHMbiBbj~Pa9ejm2oT<?6TSSm#c8g4pOZ@~NCr=IP9k1Yi$ zj4?&6!SL=7u*<Z+V0nK^apmShg%t~s$Shz~lxi%kKjnkLO+6t4baK6Zo^%TM?eTTX zSkT~rIX|_adW5j2Kx->*;=s>HS2u2ws1gkAXc(NF;DGyy(o6%jlM4U)`v<Ay6sDN7 zTE49Mz1H-Z2^V79Qj4R5`%)j3e_F&TU$i+XjN>Us7x(&a-Gqrb;|tDO8b{im2GQd? z<I>!8CrA06v|rRciG~w`D9fofVNcIGY<3`E9SIa3jBcz#N74Q7_IfMg<n-#Q=3hJV z73Zl^B^z~fMU25$`#Y{iF$qcG&XaJ{(#iUH2d;ee@sSZn#y{pCC`U)OkaxfFC-M7j zk#C;sAMLb*k+g%0h1tyBY6eJh1i!Gdy3Xoh+*h7SmlH0WHEiuMK_EXtkv40%I?y<< zk|TLk5%?%e%!IFL8If5I#T%S^a?tnJ<;{{kBY8nuo#9_<Kcp4r!?{VKs*j?*o^Lvm z0#Jb+CY3d9rXbm{P!ZAK^i-r5IXqCFS6qB(UqP9)bEj7>4c7*7pQ@_y^ZjgTVt}&- zowEJ$@CNB2AK`%({NXR0M7Qv1mmMu2bA+SL$(+NF+EHP#RNL8#&nS^{P&0;SPP9l& zv!gd%Y{lI3&Q^n6LGZ87Zoo&y`PDk}Mk1kM4pLP?`zWoaGd(hQAMK+O<tq8$?CsQ* ziC8XJdTvSPNWB<L^$>^6iTe}u!;0mVjhIbsXMXs~t!AU0lc1f`x$5t1YC|^A^Y3V= zA_ee%d%l}s*b3RW*xoMmt}A;k_9RpCuu9yO$Ysb!x2xJ{UQSt0m%~{ChL19WA9W7e zx*qj(y?jp+cVM-*dwBWY&qUKRcq}43YFK?^vs5Lnjy>|72Bv7x>{D+qJiBe;NhYxi z`aHOJcx6@JyueASC>`XskmLb2aTjm#!DO<+Re^=UU>NWByD`O??RkBJ6@Q!;_L<je zPl>l8@Yjoe0{GbbcfN)d!~~*MuYIdvX&b!D7J42YpZDj32#M9K5ib&if~hFI4}F5R zUmp_H)^=^V8J(faK1!~3?hM*Vzd}Ry1~n+3KnUk{`L+zP>ly98a^$hMK!-2-WJe*4 zQxx&>6L#}oP%)_yFfGa@VD}Ir78cBGY$j~RY)o7%%<N1SEEZfQrmQArtSl_-9BdX` z0(}41kCdPaFbRP3e=XjyFG|WK31bHDxu6!p!mo;7>eu01B4J&2xuX$;<9Lr$Yt<SL zK$Df0u6jez!wpAWE)KRjmk|^&Q+k|qjZ7sl?o0|=VgnLlg`Jy<<Z{mk0(yRJsR3^u za5ekpozYO#<#^x8%+%v(lRq7?wg(A302qh8-<=UCw`c-=mapIuwU9geHkG?n_}7$P zPx6mc9~G~l#tg_^oyt(Z%ey1eq|x?fR@@a+SPd2HG~0^2R<waymj4QD5;9&hD>x@B z1!R}%zP}wi`a&(O#=yB2gpCO(X|Cd`V!ajV!YEP3B))2Sh-mVDd#z#V-D)!kc&ZiP zP?DBy;74*o;ZPZ)ukU6?9=PU$$S^{=4C|_;c^(#6#mO)hyo|x9<!<f;<3bHFm6hww z;{w;+lOhZ%sAG@rtK&i*F(ruXOXEVYG}X-vz;Hru9vI_-DlzfS3|??zm>xi0MZ<6s zpfsk^`-9+w_G@^k74o1K0lB{q;DS7;qx&_WB`1NxFl3(UKfz3-X-Zo?DBlXbvIo5x zt?Nj4J(Sg|OR=%@fh;vGZ)so5%D9}?v+Nn9r*z!eJ@>B~f;Naq|G}b+9Y%c{yS<og zI2|#`Jw^ZF`)s->t$F6xnLm4ox&YuhmEy2WsQi|GnSK+tOsM{*e3_mDlua8BEt9Ce zeNM0g<CSA-Zv=L4tuk+5FWpeV+AbpOR^c}N^_fXufSU^Y=FYwNQYcBXVwuEDOXkVc z4Jbz=3a-{?D1$$_LCw^K-ca@GA25TrWI&UQ(A740uf6mtGSQ-rkx!qaDo@+wqv+Q6 zZQ?|o-;lmXS)R!1&Hr4t+tyn=K>cN<UO@M0_s0av9kamD$t!xq9TrvT&wn<&Q!fHA zxi?El>L4kcH<+T741aiYd$a$4Ui+WrVDj_7V_RcqR}W`%3wUNGZZ>u%cnS(}MG5%- E2ag!DvH$=8 delta 15147 zcmai*LvWxCkcKC=ZQHh;i6)uYw#_fLZQHgrvCWA!vAzFs_q0`g>gq$E8c)9+v;&#F z4Ow6253q8v2nxbFyEvH|+QNElT<U7ulXJQG&DNd1P~c+gk|23{XwrE}H)@ivr)^JV z{Q;pL@9DR}H*kkH`Mh>Uw3lccJ5OCQj)7teC8@|9F(SyFbhrCAq>p$<d@AHw?@+(M zl>1FU=vQnF6n+ElFDGqbzz0_a;zI&R5t6+k07Zsno!uB#1o9@2=j!qPa#@3X6NC&K zTpuTD@s;Nn=H2V&zBIZBeH0>075thD?D#%E33<4!PhDZgOY(VnWvdDeYwmp^($6|} zg1OWE_}#0&`W&P$Tolo^o4pgAOEN-Q{M;@mR;CJ@sfq1{d)`GRB$+SQcZ2OmCU*T7 z0FOK3N<?~Py!2rHWdHE|$f|JQJ!;sKP3IFd_APQX!!v`ir>+h^*pKFql2`Zq-9AaN zk-e|ztDkE+x`g7Ez=?8VFShTop>pI}5QE`KxrnGDE4)#f<t{qt!0DAO#cbNzd?8gb zvfna1^lM^-Y@u-B2S$Xbczjy|WkBTvU^cOL`Bs}Sxo>cv{v0nA+7lfGQjT?C;JCn> zrB0@Z<W6lj<V#%OP<<%Bs(eeuIsJw0nei+-6yItQ;iPPq_%W1)vL60OUikB{=XE-3 zUe0WO5L(*UFYV8o8EJ<F9YZpLk|~%DmjX}KUG6sv(%l2PeF~XORjUkxWFe~|aQa<Z zK%80Nb(^n?Szl+^&D#_2?<Iz(JN@!}fU$sVMD+ZD@dOVKnQcSpi&q@`<eh>wbq6ou zCh1)uLj+Ue=&n933J*_vJu>Z}zPw+}h<Cf_K-!W|m6AE?!<H?@gj=1o&A-if6cIa2 zsYi!38oBN>y4ZQ1u-nZeYaAI0oKl)oLRy+PWjQzXdEXzG!|!|?=Y_)Y()N#VBX=$% zRt;L^3LE#_sZ$9uI1TGgi&w`I%COLM$5fKgmNlF&M-}kN*ZE{ov_n{;c2p5Kh*U)@ z8h`mx1F3#3A(m85e^xe4>0X>VoCh2pjMC(-^M7IX=i3C$2}qja(O4t`j^s_0pU*K? zX*S@ER<T8Gly7@1nR=YK{O?1?-@%sx-NtW%Gep8sd*+DlN?HvXw%ME8gXZ-I;!}5W zO!2G>L0rZpNp2t^qrKuWE~z^*kl@Q>;c=3R?ops`t5HRlHTid*@bJ5XOquB;4~@i| z2ni;spYVa$9RtKGSF)_Yo{3bw^wX23n;TY-l2s5(ifOA^GN}x<O{3_Cdk8MsWNN}# zvb;y46hsM{psCtP##zZi3NbY;ESgZjty5HjM{$I7BeYSF1QFU7`=g39W2*tSRsC`! zIdVqw6GSA?5P5RsT0M~>Vd=%<AW*sFe^nI3zaGFZp*RAvFtG)oLd5v8hSfv7&kGst zm_gK_DmK2{eu@ZgVW*sp6wq&eLZs-Xd~*_JKco<L#qC&ZF`*?m&k?K?_ib02)Q|y5 z%|93>n4oj(r_WdJA*nPNn=Yof?p;^<P_#3OyT?!@;3+9+hiVq3gqmPO0%=IeMBQ>O z`iF-Tk|vl!%>sd)nS(k0)qVC-P7sE;!IqghjsRL3)3t{Ck2!1OR65a9gRVhNvQ5qu zo9Kxy^qh};Oi^qDD4AmvN}QTSUqq7RD!z|+`t=0<xDk{&JnCu_;ej(o?tJ;|rk3y; z>B$hx(<wUJkpyaPbJU0xv-jJZp*4T*!jMz=F~uYXNo4>E&)gq^H<3}iVd{%BaOfT{ z^_VUGkI*zjxV!#7=3)JB2c!jGl33!Rm4kIn$J<j{L=5%iZgUJ%*nh_sd<6MB4x7<^ zlwMI&)d{u4$4rv9vIUV*N5`6eTkBZa&_#ODPBXC~D15MRd-JJE1;__9)1U^?7i~Y; z@LiNe1XcmZ+wOCMu=u$Gwn%EEW>F^X>x(w~XBD^wRBdF=u|fj{_sD~RV9caqM}F+e zY|#&%==Z{WtR%A*?zea9-y?OAndZkeiT`Cv^)|C-O*9ywc5REnZQc}G8%*e2{)%X- zOdt|MfnlWU^fqS~xTR^DjI&U_KQmG`raF?aUk(Iqjyq00%j>CFDIjw1@j)!~lxYO3 z%-9fUS0_^Kjf;4?Std2#@iZj-h?1&skFdomOHS6#BXl4s{>$lr=0`kqL^d4lH^L59 zBHd{5JH*2@#ZnsFtSVWAYSvWc2`Ze4#OB70Z>2`VcGQC`SR<NQ?NSOG{C!ombgENs z4HiIFM*$N~OzXcMU@WlmZF%u5Rl@#b<IzcU0zkw2qY??txK@CqYhX!z_~X|7OU83T zmL){kiAFQgdYLM`2hY&2PBt@bjrgshm9#B>(YbU+dQ|BLx~s|)i#()hEPT+<cbmL& z>VxI+eUVj!>fy|#V2Kj(%e;hyvcV7)Rs+CN?^g~`b^mMJ$kNX=dO7e8SFtnINNd!L zQGMjV;C#N#>>=tP^&+>EC8YS2Q<LQfOZCkUm&MI>)bbPOb;!f651I&llj9Y8JTmE; zTNsjniO)Fd(;L;|1D@33GV0S4)Qy&~vnIXGbd@q^THPEc!B7i(yf~s!TS$={p#*TL z60}73aUs6yFP5&GYyoGMZXBMsI>c#tT?nl;kqFnO=h@6beBC;#R176f7rEJe2kF$_ z-sEF%tHSd%V!UlYFW%zYj;|Cp)A7v5irNuiBHYy!3WW8_XXiy9g2A7{ys5MAAFb(+ zkfO27>Y>vtsAI}<?N(WtFiOl#90w5C1@(XY25EOen$&Exka}y`&G+iWp9tS~lWphz z=UhT0yFgi6)ffbFCOi8J%t?^zS5RXw>a%iJhPrDOs$?9+MM^CvyEGVEt&251xvx{D zlVaRa1FhaXW3OF*xi!5+E_+<C)%rY%RvNM+9~hXoc2&b7F8zeyZ_tNfDRLlh$A%g# z9)ypo6&t=PSx{SS?IS`*Aeo!7XN{71T@nzT<AI-L$%nIEDMroamuSztB>xnfnkP4g z=^;o_L;EMq-UKO+mxORFn(O}1lvFm9J94(Ptm(=kC*y_<;RnOo!+Z~=SFkJZ-^6A2 z#5UhkhoAIEN#+xYJC-VQ1O}*?`3;xouh#FEw2C>-LIvn>hgjh$6PflJwrPMfOZXhv zE7F65_$Um!OZ%8y%csX-&I71u0BD1prx}c9!!Uz%O76H7BAWTXymZpdT|}%IQ#rM7 z(!1})Vhg%Z?0wMQEN-px=H(!(X}#=UxCvZ)`sSY4bBLX3ubWG^lE9++5pix(EvSZ} zigOlu=GJHkd|>NPwI71zYZ=<n8%lF6yv;||D8|2!un)x-6R-%M+>l$5=q)>AXM|*h zaU=GG&xLNR^_JS3u(5C>h*VKr)=DQP*8N5%PKK-nWh5}N429<l?ZbNM5Ax!1RS?D@ zo4CLGWy*FR<FLq7+JNuCr&Nvku>!+FC5P__9<v%?(vkg5E|C~tL&gx<A7Xwujcxde z`@t8;MU#q0uaWfGJ^7L}NfuU2#aB3BLj0Q7G-5S05NXz+qLrwtl<Uz;*sXT8Vdvdn zfuE??#iU1Q$448@ZxTh+=SY}xM`7|+++LIQ$2Ly|V^d%r4tQv+`XnC6;m1#=_t=k1 zGQj`TDmK+3)46>LgXty*rSlL)elMzs6Qqpz!O$lk1kW%4iZtnL2sz@2Z0$Y-ALN-= zWzL@QR~g#tez%$Z(r#zgCFWk~^z%Nr$VN5Goy4>jQeH^z)BxT+He&Li{F)5gmr6L! z(hxJCFjBrw8!$N0zA59c3e1ox-KDJoJa?5BrbZ>UkZW89$i^oFLOj&%;ldaZUTb{y z-o9jbteChb5nn{7cLSsd`eon<H_bXW<Y7xDIw|BsQ*KL)y0Yu~anVL&vzEIl5&LU6 za31cC^7q_4og)*x>7w*~<O3@RZ6`U^b*K)Z#C`r<01<`DOolxTOkU(zCM>cKNB_8x zn&NqT_}Z+q-4C~nFyNj?!`howSPN4<8+33J1OgvcaYiG<1>-0=X(@_1bslLD^YdZK zLbZ$uOlOZAlXj-Z+HV?nrn@*^RYqVAV3nJGmS@MX454qS4!<gQ*h;K@c51}#xI__D z+W$;92OdTJgk%W9-jY<qhdK0l!aQbMYDeR*i(OR{yHNuJw;g^P&sBCJkEcis`Kj1x z)wT+btf>be%(J?2tkSdd={rAb>f=8lBL1WNSM#_yxZ_!f?~EAWKyXCnm`#rs79x>H z8iTw?#bi-V*5Q}+_f55hyn+y}86&7)$pek?0npXwXW9Q$SPmo}vp{)|K2ZOcRn=i{ zH>TofK7o1qI$N&Q-{HM8=yI1vpGun9{CATj0R{6&#BqdZosUeL^!w>@j|mD_IOuWj z8(IKlQ(|BmC-Snql<LcaSXw&G*83Ge{C0g2qyKXOwz*87`2!NBJZ@*O3-9&OBLiQm z87P5!GgKB2m#n|VK}WH}hx#+p5N34<%jC<IOt0lg@4QaFy~Mw+b@c%yNa5ewsuppH z%R{mNcHqWHY<j>dsY5`t9P2pP$)IL$F1o=T<kWV<I*l$Nr%pbJUMWb8z;|if-nI13 zkblJ`^|S8M?=IP7?dN2Azhz>dR_JZUJivjT9XP1ijGBLs$Pc3xcdz#7poh>Li_*qY z>sxZo<j^EEHHP+C54UC0#Qhfqt7AQTj}*MD?)Wgy?c|d@c~2){c(a_O54Q_c`dkZ7 z-MmwBb|xn;^Gtk)=aNE4?#28_qElVUtFSZrCe_Cb=?+5l)~0b4rFipHP4R3-1Tb6X zog83g?VP~oK+mBpPLDS!!RM56cWF^Hsf~HEYkL}B_~L`QH#sC;hW1v~IAf60e05z2 zg_R!Jr<_;}G4o%(aTaA$T!2}f#uW?`VUok841E*a*IR3Z-xF?>wFtqL)VKPcDWw!! zStH5Yx7F5bN`UMz@Cf-_;6olA1LVm`r@o2{>pY}13@;4B`hmB0@;T9?xub}BN7wY! zsD@Vd2%q-`o4H9=iQMJ|tvX(W?ZSkcsX5yd1+BuOil`>E+oqG;_Hw6Q?MX&xB16v! z3drO0^S?L=T7yLjwH?Vh$j%aHv$VtA(`%lIBQ<6flh&(<Pq!7Y_o-OZz$9ZxT%Sqj zF@{NcJvp+}7@O!+--I=^<Nctj+*p=G5yvKR)|Vi-ey5U>Y65n%Q#BK=Y|rtSlZ6*l zA*{b@9o45g6qvETD7SkrY5Vq4)kT#4q3Q{4s9)Cc<JNvLohh6?=PMd*M3+fYnJIkz zIO!%2L+-xbSLf-Y#24Biz%4743rZrW=_16h`7E^A#TDfU`%sdCRy6G)qhU<deDhOw z<|P?(dcd&zFh14lP~zXSLOG5)N;qTLn9iso-vBn0dQ@+Z|1Uj44}7)>$cik1Vn4Do zNPid)@^P|$H7De6R=q}D=+Yve4!^a%n7UpZKJ<J7`H;XoJFKEPAk{hHNio5Md{6$U zv0U?5)_V^M!Qz<a5wZY;atlSvY!GK=qtyB6YE`9E^y*gdglM%%OO!9BLd@^>Bh;xk zTcv|!U~QA5EiVYGfMw!^(xiPx;|*i-CDBTL9g@sRj)EdR#@?s(aeC;Q)Rhs3>-i=^ z@l{y23aZv%V!n|HpuR6qt$iYB-XTX;vFe`LNwu^6mDiji6+JU#xpSz4_8TivUQd2e z-a~8l?*zj^4qC9U@rAK!NwJh4+P!=)E?Cp02yxA9sSP(wFnVOGj}0o;NC|4VPw30% z&L{N?x#~*j=O_2fK>X1$FBa<>Q~g#QPSYM))nA{fP(5WWfCj)|$(r3RdSh?>r)qHT znZfJ)?^nozpOBc}M*hH8!lg?+weex8Qm2s6I4;P|@O_e?T;qjf?cS@5NA1JjC%KMw z^5I<?Zl^-Q@6B1{{N%PKJ8P+(XnKtMx`<-RkAA7BJ9Q<Wy)dQ^hfpHUUfXG;s);Q+ zTCXFpm6=sZphoKPtye;m8!qVgA2)?6C<W^_3`wUP=V=2pMXD7oYPwAWkBc+>mf$Ew z&!hP}w<saFmDr>hq>1{bedQi#q?PADrZNXg9>!ZkS6phnGhG~oi&4c~M`koJ6+wo3 z*F7_R(4*q`lbM?RT6=BG$NS<i9m}v~uCL*4IQu>w0H)IqNnX96ll!5B;9Se}V`aV9 zvQ_@?<Fq;C3Rt3^!0nS^A_4rP?d*8UGKR{h=BxF76T|vZAs1JjuWErs8$RdDa`a@h zvbBUF@V64p79|9&WfSJ2w#B^GrPla)nFHTCaX3y&TqC%lBKu`^AKDLh;3Y1h`<q`h zP~U$NaP|MGPd%<X(HTJA5U=NS0hQ)~du8m@WqQBW4<&7Z-=aU~B>xoWlF&yN^0k~+ zRrq=}mdOg?G#`%cB^8z>p(SX(b%Vn&(@M}&LwOj=P_}}ZGY7cp?`ukpfQp1BAE@he zUB%QXbO~rfj-TJtgw1O<Vegd)sKk$diY#XWR6R6%XXd=UcjY%bWxSa_jH%(NOV|L_ z--Om!Xj>h@IDS7QlAfx~u3gx{8hq#7tvKUFGfa8NMP0PSxg1$|5}ESKx_p;n<!Xn+ zKAZEP$>m_aT~{;wdyNVwA58I%=1jI~I0<j7OEK48=pIH9#5pq$qd9s3QC8utsH#?= zALbBUXI2l}nF9F$Qj_Ej-N+uVHrXbF2U_l>H$cU=F_S*w?(sz*Y`OL9LmtBkqqoKK zw!u%!?i=B#X!*>c!CpZQZuYJW15TLHTON8GeU)0kT7XAEO+LwzAP#TY;ZQ71=CdCY zKXL&{naC%?!x1pQqWN`1CpPiP#NYv79CEjV+UXHAt#)_5PDmfY<-gk%67_p86TYvT z)-5Q=u?l2VhkIAX6Z|rKnIa;6G;*Cv*vg$8^=QF1AMd)dA1YNf+d|th8lHm;x#NJf zD&q_G32hSeet@Q~VB}_3K~=5wvl*IP@soKVd_9G2;XIF?$4BOEQqWx*D({xpRiX<# zIDN&Z3)&i#?o8hFS#zpQJ7I{vAeTgDcR^;m<YNA;<u*?6{ws}dvMJ?~3_dtUL_X{V zK5Hw}d&Ba_#RoG$=wtgE%!{S>Z&F<fAHe>9c&7HxIQ%x0-V^nQ=`Q9>GmLRkoES)v zz+vI|D70--BGMWve`E*;6Op?<MGT_tX~HLdwJuGG_~4PLhnrvYYQB%zdnX`})8B?S z+#cby6McJ++I~-pU+;b|pHX{VLLl%T7$oa^BZkCExq-Js(qq>Eea7C%_O83udp%K1 z%*WMZ&I;t~b$$z2jN#j8?*i}Xhn2(kL6p$sTdU?SZDX#7x8Bon38cGr=)9AL(vDW7 z>Dv9~j&gnqQh5XXTS-^E3X0E-=~SCGoFy#Fl=v@#)tk}Ed|PVqTgTg4!tBEOLchBy zut~YV)f9}^rg}3VbI9hWTxE5Uz?-g-MdpD`hGJu9G;CM5tk$I}ZcMkmrn!+94$Z|F z?l2oPTL|WbmZelyo?P<6gZz#JquLsCVCxk4Lh5c{<V-+bu;}p}zj36&m~5kdLE|60 zC|N1+w%)eTRmqOAeXiS$kWM%V%*^4EH*p2gpNPd}9@JYv@zkpv9gw=2Avq4c7c+O^ z*}wPbqkq;l)l|Edo{!wG4)W3Kja(PV@?$c{q|{4U(5jHEbYBr+?+=!oT^fwDn~+iO z<z1<s73NsdVOY8Uj|&c;#gbfAF#HV7<EG|^S3^&mhgGMd+>?5wb~-GSJ4>XnqYB%O z-*wLlX5<6FPv`mS*Z9%--Z1ESn%txFnx5`6qrhJS+6Rh8Kgo)?W;-u5Oy{9AYJ$9o zF?wJ)>9KG{)-B|vjUQLM&@*a}#?0HukhgvQF)^x#|7}w%bFS*^-fowH8qGMPG%wHq z;fczBTxEXWhO`tn>SZ*4>Jk(>7tI^}r~e)$W%>gF;AgG7G{LW&A4@lyqe0rkRu+$7 zT{(d<!mw!(f^`3ho_1}9F?o|Tx=ArOfj?RX&RSSo?SPXah5@#lZulE9$8jh;o}RV% zzW1zA7az&q5J3*%Ib3sp-bZ!c8e+0dXNe>~2cKxWjH}Q02F_D`rn{irKpfHMWr}0j zp6F&8xD4N6)1RN{swcTd{_W3vdsWpBG=P2!r(VK!#<vVUq*`ANv~9aevg>(<CFCv) z`}F)}`hD<K=Q|G7rbNW0%pfP`;{f*<@APO8tWT<*=kK95^5ayIRL{Hdr@@so_h(P- z<toD9ylAtci*3`+L+g=!f@<gi>G(sr#atIVaEs)t`yAba|8rY=wNAN}lhv5DOlK?P z*^vZKN_-1h&w$5)x4kTRr>gz~u=*m@*&(_pr)vGGh>f_Yk%!LJ2a!{Y=vzvt#X0jZ zmy$wVU<{i;4$z$}(e9AXWj8uO+!&E2K@H)!wh1*3nrxB8IQq+Qva$);>%~Pc*?Tqt zK$Agea@HOM(wzJ#rB)JH>M<C}>pK0pbcdoeVqY|2ddvzkJBg=3qC{7dc|G#>LIeL% zNs|{+s$<8e)}|fv2jW~LGH?%!v(1|zlPJIedPShrO7Ma*Nh;`<<s5X4bt0TcNwZpI zC)I>C4TVo*bE;4ZD|w$0qgH9BW6iH|Ko08tchha>KQZrWiYcv5Inzbg!p`JN*_txJ z&!tXmQoM~*e+A6ZLRd4=I5t-nOnWq|`HN20JtBR0A*2cMr({9+k3xE-<mhsw$UjYu z-L^zQr1JD?-?(3#AN83(g$wyusVz=CE0<G^8HT9Ygamlls8{R|E-D^xy=vj_j1$gm zXzU2v(A~9Ai<Kq<>i^9a6O-lC9GUkKF`Uw>7^a4~tfo`^CLaa;7fF6@YA6s_oj5+b zc6vNZQlqt+hQr!5;i9K589BQ2m<DmPff|33M_Wm6-DTQ5qqP^M7Vcomn<SJ)0L=I# zR*$odH1O#2f^0udev5P*_;0xetk)m%h*4EDR{X^lPXl}3CWS{*5R^f%(j@5Ov3ZPH z!`|kYdHRz$^GeY}xm&Zl6&Tuvv_k-qJ*TF?BA2qbV2$!1N?jR#e?L^Ug=EMur7@i6 zpuXvX>3UnyLLwW|gII+?mE@N^Du99Gy3aYlYdY7_QDiR2j_)1ZTk(;WBX8GLFX5gf zNFN!qvf>si_h-qIoIQnO#zHR5X-O8+IP9*4-E1KVCz}YkSWx(FoA1-=juX{-Y;aXN zhS{re-62)zY5=+knmznIaPO;r)WUSzs8avHU&j0%E$JptHmcAUsJm&%wSF#-VORWm z&+V-~%H!v#EGob|lR%X{yI2M~qx8#bukmk9&e(^`rMS_JIkW9v>8(Xue+&P!XulEL zC^}!>)`uD};1N=>Yt3mX@hg(fx<`++GK{WVZ+4_gmFL=BFQq}$bZ4mKUao18roauH zvh657tLkuNp?o7|%{6>og3Y4TZfZ!a4BOi=Dz@j}M)sa2Pl@2A2w&@{4f!As-VkT* zW7;$)p?m)pA2v!n`ic47ctFB%rpK1)fy?H5hFv27DQ|e@U#j=ZGmvryp+(df)<m>r zUt~5>m7=LV=1j2a-BS5NC&jQsGqukr7Uu6JG@*1Ms^jn)jtGoeNK;>zZ6G2ZJ>RXe zrfV(@fh6a{gr=pZ&!qnZA?)=*YFwJa2km#gMhG_FSeV8WK8&5<LrA18`~;|^=1_L6 zfl7B$a}G1mlK0Cn->jiz^v}z)<YB~EGox<wcC@B|=7GJ7CGuhdjttGC_ZEp8^-RGB z!COxkzUpDrS8(?P#EMC*UlVnPUlcE-A3U~I952BWBqaoOJ)VjW^?Z6gm0T3t@|r*V zpT6RQe+3&RxK9elRQ>`M;)`Kp<;?-(FoHHRaBtkeD_Hw-6d})sK-TK?dSFSjuztNH zOfF89Gz(`&(iJ}V-vhE;Xh{|PtTbE)vZxG)_yCIu&XUuUA+;VUd=%a?8mFgsx`}hq z6bbZS_8b%tgp9}i#<0P%Ql3I+QF7hsoS14~P;hH+rEuwlDJRP{(&bpR!ify@WfRyW z7Jgm;C=*tcc&<fIgFv^<ReTEXO~D5$6Vro&^-bqIJ}CTfG-00Sg$&(~fV#=WEzYbD ze!h3>ag}au4_X=8#FN82d)8wU`MY#IdDcPBDVpmMyV!*?XcVi=U=mUh$W2qIu5)YK zV%&9dNptm#fhY8yRL`iTXRgYVoKF~m*M@C|ynTmLkio$+%X0%Z)7C-ER>vKFQK%a% znnU82bZ19f^wWyDH@|~Q0lbEn)1-tvGQirSWPI}mL#r;a^EjB|gDKyH?PEDFSrdJB z>jkuh;(B;b9k&I=iMK8qadB31$KCR8TeQ9*frFXUYJHy=3%=<xH+n6fHF&n)KaTI> zsS+aTQ`r3rA0x=eL$fa2sbfVBn`#*t9HCX{N~Cq()~ZZD^m&LpFwN8x3vFNB6M&*= zkTJ5rORR~2<YJ}K=FMkP%2l{?Bl!ElmGkD3xc1{cPB+3e5^1)-3IEjr=eg`mjK5({ zc6qfgWZ|^B%dF?wbU@I^*<(s?@00i)W-*?~gMRzNjVy+|uMr`N$geR?>|1)dj1W57 z=5t|I#&`2scdIRvIP0LjvW<tdTG%Tq$pnp3K2}?1ki3}s^^R5l)QMXvHA2$Ul;N4B zuhha>w!gW8_7#IZd=HPJZxk<`CMI|icN?kimC2MalQL<b3atsE;O7;<_P;09X&r0l zP07^H-agRXl}Z}4Pd~X59kR&-4P(Bix0GRg-+T#avk+1a@|3mLM{fl#X;5_Oh}LGj zMReTLtIcP}tIJIUe`Soq_|o_dj0KE|KcW|+-oO3^Mo^Cq77UJ&QtM)?iW|cPAr6KN z<|n~(Lm~q=kOabXorAK-Nd@(t@r2^^8&Z~V)^HT;wZ`O@zJ_82zmY>0Ls)k(5FZh9 z2zYKQ9eR~WHbBKJNqqPEbHJrc6nQlBBUT2`v9+}4Zd0o-2H!=YOe2X0fM^Nglhe3T z$s!;h`jp7Wke)GA13PZ?mngU)EW9Pe?|@phKo|ff6BEDiM`=sw1b8v?gs2}x19+|Q z&lMQyT5womhF`V<9x1S@1HWX-Bb5r5N*xCCVK*ES-`G1HCJJGx6ri*qR3R%9+s~`T z@Upp~3JP>iLv8UZNj(yj3Ze!u=322}tNHNf>AmnBSwaVsNMO_iT$u(c)8chtAtY#- z5yt^vBM}XB&=`1KYZ<ztw9*Vi(Y$sr7<=OGV3eK$aLgD>i8Bir3t3ra;{tn_V9$#I zgit4?(q!x{OHAR}U!3WGy3&6@ywku_h#=Jz2(mw&(qeQj)}kss1XK=0APE!y)yRjz zh~!KV_3w;B7u_U<h6Ry^N@$1#4I##~5P<<yz%z+a+5HoKTNF}*af95=!^k4QLMP+) z&o^`Dh#trd7K-pC4k+<1WMWVB|64$IRYLgy4Urx(q^>IGc4>1#@d<*Ur1&7`rWWPJ zJe9u*{u_>;&kQb2>WCU{38O|j{?kK#2^=FHCEy*@$YM>~YXVIF$B49kYO_CuAF(0e z@`G$RmeG?Y{-A(&E-IH+v<*8S+=3Ny5JC`>jNKvvn?#yCrJrP)3K~Tw2R0B^3{1U0 z;ej1-AQ^U}5rf3cKSIZ!!^FV*MJvI^5@tzQd{9O>@HfF%V+RzdCYlF1wK({csa)-; zCaDW{2zm}mBFR`h>=*GAc@ipK<OeN)@U0XLOi1b(GkidoNW%;7MV2a~XsI-p9j8a4 z2s@LPz%V2DQbt=q>Hi)d=rLC^MiNzD59TZvVZp`?MNBae8LA4-ffn9G7bX}Y1p$?H zp_h+Yc>dvD0z-iG!NMwz8%>BchT*F?pfMaJZzl;Z(id4U3PGx?l!woQii8ei_Fiy6 zrZn>v2?PZ^_vgtfg`1?hkq!R!s>d8DPJ#eq`y~eASeS1O`2!2I0lk7)OD2dFlus7Y zD<3z27gOWTgn%AaB!=Y>jQekZSyOQ?{HY<iM?Px4)*OPNkOgR{QavI~y-7c8Ep2!l zre!8fJ+h_>XpP@XfzR_}BP|j@m2_6<<Natk(1cYqZhv%eW}`9v26|t>O_P`M=Lkh1 zKRoFUd3z`IdKdrx{jU)-E>kJcSB=@UTXieM2pQE>2Rtc!^Lsp$`>5nFzCmvZjB*fH zgoO`O)Se*2qFgu%<nntx=(~^oDI2h1dHG`>wC=%vrkkDfs8B~)q~Hb=Ur5Z<Z#<KV zl#3#j*R6Z<=Fofe!-psACM&Y!9fFE#F*?i`zy#~hmX_I9N%Z-A9$LQEzBN+EF+rXz z{}SY%2|KWl|9zZ9e-^jszIZntbS|VGG-APfHlC{^Q!*y7wIREF|GRNTAmVja`Al;6 zVov#qz5A!Ngg2_K0HiNqtAlie5F**Bx<J(ZE26XfjJ?C+l(S<jT?va|n;c7En+ywV zn-q&|n*>AT_o@pFpoukLAg|6MP#HB9|HUe~H2ADzkZa)$kBK`f{zF($VtA(tAtV4H z0TD7N0cXcZk%b`|MXZVs*Xy<;bEXn5+6M0wL<@VN@Pb834VDZLb($ZtX*!Fx9%iTC z6qn<Y!#zC@mI0HZ6K*yPjMo1K`b}zB+7Jx}p1Bo`6E9$9nnfS*@68~-@7?X`c7<VP z((km_jqL(pO3mZhw9LJEgD+RCGA(S=N{ecjci87QKoKT6<#(ZfOd8y-LjOTwL7Ak& zGm7J3n6K#wM8gFLee=lh)+CKvB(k`Vf2Mvx;JvQhbM9Q@A9{;A#ZWUhRVHVWxI#!@ zyK0yu$0y5Rl0u;|1eK4YGgu5WcU*rgA~bXOXE_$37_XGu%4tu_l#$i{gIl)0t)?_a zm`??%q40L@w5gApyIYlUX^!auH<!bjD`LB$deI#AF}wzr8-D+&q<H2-zmtF@+=NTm zB+NB@(KCfCBwOKkVGhEG9gWv1$B`?Z**f@LRCtBM$ef<;z$HUmau6tLNE+@gu-vbU zN4l9y(Vj-8eb|QlX(zQ)Xls%2Q(~%#a6P>hwjtZvbUkWthc?%xj65fIC1=*n+hNg` zuW(A=_?!)Bz&b6E)(dji`THE0Vo8Bo)ayKz{wVGbBmDEqbc1j;P2@3nFO||svneBo zonekyXGn`H<il)cA;WMdB!bsq1=~8#=fw=C^S<_KoE}r~OG4RrF&bB+wHSesULYhq zL{ioU;#safQ2A=6p-pepV#G3HQx&v=1*@;p9GwfOfJYnXa%)eWL!N<4<79WqM6=bB zkY(^X*7{mR$YV(FppmuJRN!D<YzTd;f}kJD&aT47K`yU{9PON-$)NILvQP8gKD5vt z6djt!)w)cldRktJnjf)Xxfb$Z74Us=V@YQ~B*bUp?urUZx+@!ySgwq+Z0{TqS&CtE zL{0*t@my3&DkCyErr*3=tWn>H-ySn~!VU2Rv={I39{z#YFIG#pgY8sn=DdOJG_H%X z;y1_aP~szcB$-Rl5Z<UEDQf$AupRNfhMI9ndI;jqytAO}Gq4eQ{GliEg{nx^7HSX1 z$;xiE@`S4#As(Czn8Hh#%<ax{@r~D^v3din<N?irO%-cea^sZ~Y|RbZ->&jYcE}Xw ze)2>3WBd^e+Rkkba5Cyi(Rk#B-W03s2Jio9U(ug_Baj#<n%b3Jw>RV20~9}H(&E-P z7q=%bl8>Q@$8Vsj3iX`3Yg2d-t80aG);ICCizE3YnW6q`w7NuK6VnNW^Y8~&Esg*J zne{fyOlOFoh3!&}q*ZG?j}1qyqfeV70_KX}iH4m(s+H`r%|KV8ZD)NaN{w}7BW{Ny zLL+X=rq$&<8>oxzEx%NW_rjTl+nGGaV`=BZC}ua=#xaT)o81BKgV}#xE}m8SVGivZ zOzR}ZH1+Pyjb6yy>Mb5MFwat)G$50~W42Wui&bN>b9AO#zt^|=F!mw|k)RaW;uBJL z0-3Wmp{(5zf&VBcdUK6AE)T`f3Ve;1^FM1ZJ$6$0#ii<srV=z(<G(h`((rM#8rQA9 zao<}%rj24trG9WLquv9fF*ru>sPRhdWmB_C`QYDp`AGX<Fi`WT<cWj>nCj;F)@fd6 zUsss6u&s7_(?cA^dR5n7RtlD@_K3=++GQHcbf7W?yY?h3WyRLF>8`vx#0XTMmTc(N ziRhoj-m32p@H=|<v?$p_dH=k?W)$b^qFeDc^d5A5x-MVkOQ~~rx65cP>NVY{eZza( z#0#Ee?C9wYiHY?Bf_wylEiFF`lek%yJ%1T1x`z(qzR8yASUz1T?`m4N_SOfDmT`jG z65rYD@;1cYmLe^uKAW%$k)L)_CKdscl>!8Ps@r>MT*z2vmujn3p4Ns0s<o@uO8QZL zJ$e$GQQKoWmU`FWTAZX8Fns4Iu5Q1b_2t$H9zj#*bNcl`W*N=^<2O&`X{`H)zuH=i zrAK!bEVX{zRWmce%w?k7_}f$@w1Q>B_pnC=$g=r1AvYj@#-J2$I9_o#xpO8h!els7 zSRQLGs`iSWc)fEB9JhJXRg)yV7^6r(f>W%${Hn61MdVkO#11lvmQ3m2hwB}C%$)68 ze?w{4nJ-_Ty*5GuafWblL&KA@x^`<73!fefo1S;_xkg-yZt<QscDADKUh;}R1xg#S zDg@8iAEznx&pcpaI(1venf3LDjH39>y7&=V1PP{(qf$2X;g9K1CX3E6Ix~}*mo3%x zCL4CMtOR>9bJW0nta98!^^7Una2F>tr%VEzP0V=ir#7X4`v(^Tv!c9JF$uk1oA_Dl zIPLh^s9?y~QX)q0S?h|WOu5)K8u#ipXtfMLh{+<dJCsH)?ZvF>rF1%P9etN^q%LW* zTWgItFAcJdIByjL;m%G*uns=58=KncOMi_~_XPioGw3yD-~&<jLP7T=qjBt2&M>QL zm_v*w)r|!}-+<>xe20G|CF>mP)ixQ!!daI%HWqt<|Dzq960nNwhlBE_DKF9bkJ1y+ zzN?iN4DWHxDq9#_{&%Xd9cnuUix-QbM%U^$rUaYeaGJ>WvYEJ@?2LgZnnpIf*@(x5 zPjcGxm?p1m5*s<U#n>Y$GU2tIVc77HQlgvok&_HCRqa{ac)U^ACi0D!4W_yOiZfd_ zV962iVDV7@RQ_Pm@?jJ-&R(zP<@;NEe{<fPDe%Jj;p@V~-}R#W@g8tG4iMoV#zH?S zLPnhrB=wOQH;DcRcz=xwpzrtHeiO&to;POVmu3{`74j1>C?t|Il?_$;2-WH7GK?0% zfd2%3emzWaZ89*`QK888DQhT?%^R>_E6%Dki_p<^9PdjCdeaMWYKo#$+RC&DDbR>3 zw+SlFpC88=<&H{7I@Nuo5zVIkSOD98ja0Pw87F(2;TEg~r6HvsmkR20JfAOVi!)v6 z-$5LRm{$cNFlM#Tg<D*^_+g+buR`yQGwc8iaY<&=+eEVF*5$rD*g;u3Oyexq9Bw}* zc;?x>OO<_2e_zC{B%C>KP|N^*8K`*>(mU;(?7J?OeqDR>|85!b<itv13a^);sFjEq z{_Z^7;xT--<oZAup&@BAc7*0_FNd+SZC@;9m0DIh)J){N)+BZv!}<TT=F9t-pJ)ZZ z+H1(X1SQH=YkVh$o|Yp1^%B17DHFii!{LmWzr9pq>fedNPx|0B#3t&|Kia)2r<o;B z@ZTo@7XH5^H?Eh;L^`dNC-7Dn$IRt%cWeFj5N+T#wn$LCE3P(!i^H_Yzd0Fx6f0R@ z@z^ivUp<{suyMXUJZg-1_<AG3?Nb6-!RU9j-#w0k$TX{5y*SP#<4wuiP%!X#E=Af3 z6VLY%Pn!eQNg3V$v8l~^qZ<(||GtT5-6g7xr<!CcN#m4#g=j@{wPH5w`H39vRjFFn zeNo<f+8obCBz|t?y_sDZ<n-5c(BUM5_l-M8FlSVPC@SSKLF;0NS89xvKuq9Id>n1@ zh3p!8b0aH3%abKHYc%GsY>T89${`=IXnTph$>-y0mI!BC#p;W)V6e-atENCvkCfo> z+u<ldG_KOp?sJBHhz1+f1mZ<$k!PH}#guq2DL51gO0$gGK}}^b8o9i<$^+gBLH(pg zBrjxov?Pvq8DWQXa4;D<(LCT2dECLJC134l^C?+21y}*mk^J;M2&@_>42Esu=(q_^ zt_Zfp()$uqx({>(;tF$ObP!C1V{}F83NeHh8G$OHByGqM<#~`IJx%sKuQ3`UPX?2w zeX0-HQ=rPsyMH2BRBGl56(;x(LFQ`H4Jbu9vQfUnq;_%sTLH0NaT#D`9m7mG4_r%n zfDVP1o#XvX^;josEv}tW*Ejm}!76IZi%NZoZ??icR;mY&Dse}K%{#b_$8w&X8d{@0 zSQduBIAV}DOh4{Ov~r)BRka}rB1!GOV_B8(Z;-qyctJ?MPaj?dOT<lp3g;vJeS^86 z#1$CE02KhHUqHdd`3v~Db2Jpm{6`)=A@Lv!1Q%5pCEoRSN9qJ}q5kuP@R70LX^RmH zQX+`8%6^=aRT@U-jF`|Z_3DDG>3anc2ECPmSc2?`i-0HdtZi>D2$4cG`e${wG(85+ zvfsG78~6=E(IX8`>EP0iOkSK8Wo|YM-B1A7Fd}GN!4$~%xC&5x7Y)AR3}eLh^7kDT zBsh*&qEogR$9`-JEWxHic7>v6Spe;CyhhEe@wrIO?X3!x&jM84uN{5|X+Mp7sL{XU z;`jm?P?PHQu)WG%@Er<=Mzta=d811^6lX6sPN?8yM*iX;@bx0FQ;ZO1Q_}%;PIzx& zvTKfXfj-^>1TjGP2W5Z=BLtUD!1kHBPhrCVglc{VrcTZf{f7CP0lt%PJGS|G{*@Cp z3QHT6PWFU@;TEzc9t`DK`fL&qm<5ieE>>hl_ezVcFgHgl2Fj0&iq9kh`gpcO5>2A0 zp!SaKQ*8H$zdL`6mfIwn90zqzyG$s=$N%-RXV0Y9n*r#-Q!WVow>#?p_r1Xhyu0?6 zGsaSxFE*<<3uZEz=@a22mgQ9j-C+<x<IB$w;UiUz8#TXp`6n<k{aJ=+(;hC8vV5Rg z{&3;!)R8kkLol|Z=6~%_5=j;+OUvBk<GLg~+WSauju*Mz`AI93JfCVmupA~DdS~JA zT8*0n%mB8CfY7%myN=JXA`Q86TnFC$T>manWj|KY>nOX8lQJO_<iY&e-l2~UMxhTc zVfHK>RHyzQ3=dC%bh(pdB%{~a$dx{+7Mm@}^;)4;4_;h#pQZX8`!LBWh~ZQMqq-@V zpYQxSm7jY}cX>&RXUL`0c&m+rp<v7`@_e11Nx=E`!>38`3dU~n&WI$J79qg@b#r$R ziRT(;F+QuxF>hoSfw?LkRWZMB1IJJsfVnLSXBHVo`~5pe#{OlOLaX(>E+EyX$s`7| z3reeXeiw`3i&yL4mj%z)(b?YYb=p?&J9yM4_|F%@dXF{?dJ&F+K$im&0A4ur^jfgl z2Kc3qM%NpY(ynN7M%l;od*8LZ{j=ci3fK|wzBd|=?vg5BQgo;;Fj{&RrZ}}#a-3n$ zH!7j{{UU~Qd{xjW?~725y&f1j?=5T!_v%}qEX1)r7`aPC*Y|b*`K~S%L;UQ)OSl82 zJVmLz^-K&gexO!PoMtJGF<U-JB-<$X36##K(n#}A)T~9O)q^o@)7lh{w9fB83;(3L z?P*v*Q6K!$;PLtTcY1J-!L%<3HfiQ%J>pJ5uRU)hZ&N72))RBKTJVuWMX&w1IxNfA z)AC;2wt0FDhqa8Nwg2VtdUH4wcfG^D)=@TR#FeD|t~*|nY-VjSUlUAG930Yj4x|8# z^1GfEXKIFEjIBAl8@_j&3j5y168b~3=v*u$+SB(sne6<ELa?d!?X$;GMYBPgB&uEu zm5fy!-->yCU#pvWUvB>iEE~{QmG<m@3~US|T1p|nK%qAi&o`flS$Y|zELU!H>ai0S zbnNWKh1`ancVkc?Xpd`b!Upzh07w&x%SKAMNQ{h-NA<WxI=VAb2WR4`2LmHzd-)%% zv}IV!ua$+}AN+|&6kEo;^onKwxNDE^@3N6Ne>dGZdj1xq0qEl<ft1-vtfR?0*VkGf zeZ&dHBTF9os=I1_CaEL)qvGt8d#7J|DL}IRMBPyyl=W20l9xAKW-G=e5Q-r&6z))w zf}#(2JYS7CM?XEO1KXibcsA5(nCP3+f69SvA2~WQ;49H_6>6C?&pPYch`l2-Eoj~5 z?N2m+a#|D0(z7MAHFXos&ZX<wW+yyeC%k-^#p#`Xn2;dwMF;7<c!YFS`zcaQwR%*& zwneSw1qy^XEutA|r_=#LaTDq=XK6nD7CJc$P8DkZup@K-s}i$EdCN9h3RJ2cFUGJ~ z`6^RYQNI{(B|02mEjhVAYqZEoU3rpt2&NV47-vS8)0|jvk*Y#7GBdksGJgAwJ6lpx z93qYxD`;k%m8ml!?RLwipEf4-aZN=rPE|oq-MjO?!WKNYT2cckyT7-GePV_2Yco}c z?)I&^v2|nnN)3{2m86P&oOrSd|9qS;c578Dyg-#9Jj;yil{pIH$<Iil$?=$`n19__ zu?9v+;WzpHr$SPkl`0FmHDHwstyQC}V?}5u?aPlCI<v<SNg61-%{P2Y<*>8&-frz# zukT5)J_sAle*6F)nV9r?J~k)Y;`H6t1-Evdo+vk?<eRv*(IN)Liom%*T~Sgjw6|Mp zdYe~FI?KP<7<bv5R})X3Hk@rQUvpIa$V@%IuWnAukSy)a(;4=AW?n?x6mVSA571)p z3>6|AhW=w`_qs_R2Cdi#qeJuSnwb-;XfGBVp2p{P8ihbb<|ZC#D?G`_QwAj`>DpqP zqMz4O>fT)^Mt6Ii=cxNM+XNFre;(Ejvw!mHNk)%ZI)48OniQM7)`dZz>HPfOVjGb@ z`@$9dg)e<HCzsQuyY1n|C0<8q%Tb`=9jVs6<b2C^$D!&536UhScE?g1eR*3&V~4Pn z{rQG3rz=KV{H}XMvVAXmnzSrqo6I*Bw?Y(C(!d*9+h`fcE|@3}y9p;V8wZyWk1@BA zu^Fc^8;c>UsWA&H2dAN_k%_S&|Nj?}c2Wf*32<`%??VU2(z1%GA$sU-3$w`I@R)5- zN{w`l^tGIFVxypKBljp>V(364cdTfyJ?>a_-l8uEFXL#vzh8u@Tz#I$+wcE;8E0O_ z#UrCW#RE;Su7)MjLo(8X*3-i}JYepB{eC_SpQ|Jlv=-6{RImS0cc9uG0&v}M?u@*@ zAQK&^_{2)Qp#FS~P;;?=p!YPk>}-zIZ}d%KZO5N9;<=(ZyQ599+RXWCM+K`7lzq|Z z!VRxtfexAv!%!uC-pC<oPi+Iwe@+$ra%({?H8iabRBgaj`-4k6l)6zS>Ik+ntVJ6k z<JQ7yx39b7uApo0O|TW{3N#R|sLT9p^2YtkX;Ypkxc(%`4b8V_ViTRy0OvMBxrWeX z49_`2xP~TW%mzQCw}yAXj1To!7(W_?8$4{E*(P?#5j=MI*BYqyK6><@iZ$4>J#74_ z8b|!tKQL>MRQu%Fu`t*XztY3mm|-^e<>W>+*AUGQ@c#u}vS7X&2?77&2<pis4|L>4 zJh_Rm3}CPNOWKjK4sdls=^QZZhF#kU+YZdODxElo_@Kz0>)GfgGCl_~RF*S-o|JJj zg>2MWx5*A@x1mF>HA<CG&oI>KZ8oYO$yaOdn65V}9tq5TuT7_Z(&nXh9NklDBbNI- zx=(Vo9OX|ud$fJr@BqNbrl0iDGfCTrOaq1P(Y3(E5bX%cl@DE(`6SA+lh8IQ`X&6= zcSTWUFZ_jbB}rFJTt%l4vG2~s`pO?wZ4)hhC0iUDUr`R;(YM0Y?`xil4UW0D##NOX z#fqo6rrzU6f{VpU8MYdGug~?jXsdIp3(>khjXc%u^=*Y;07ISqM($qDrE&H3UjZNg zxEmP3AuN6oRcF+HmJ}z>IP^TOV5;{+;$I-<yJ_)h8?_)ruxuQxuoM&$ijuJZ14s*g A&;S4c diff --git a/zavislost-na-podmince.tex b/zavislost-na-podmince.tex index 18fb36b..ccf4ad8 100644 --- a/zavislost-na-podmince.tex +++ b/zavislost-na-podmince.tex @@ -50,21 +50,21 @@ Například, uvažujeme-li rovnici $x'(t) = x(t)$. Obecným řešením této rov \begin{proof} Intermezzo: otevřenost $G$ znamená, že pro každé $(x_0, t_0) \in \Omega$ a $t$ existuje $r > 0$ takové, že pokud $\| (y_0, s_0) - (t_0, x_0) \|$, potom řešení $y$ procházející bodem $(y_0, s_0)$ je definované v bodech $(t - r, t + r)$, spojitost pak odpovídá tomu, že toto řešení bude po celou dobu ``blízko" toho původního. - Bez újmy na obecnosti nechť $t_0 > t$. Vezměme $(t; t_0, x_0) \in G$, buď $x$ maximální řešení s počáteční podmínkou $x(t_0) = x_0$. Pak $[t_0, t] \subset D_x$ (řešení je definováno na celém tomto intervalu). Vezměme $\delta > 0$ tak malé, aby $[t_0, t + 2\delta] \subset D_x$ a zároveň $K_\delta := \{ (y, s) \in \mathbb{R}^n \times \mathbb{R} : s \in [t_0 - \delta, t + \delta] \land |y - x(s)| \leq \delta \} \subset \Omega$. Takto definovaná množina $K_\delta$ je kompaktní a tedy $f$ je na $K_\delta$ omezená konstantou $c_0$ (spojitá funkce na kompaktu) díky čemuž z lokální lipschitzovskosti plyne globální $L$-lipschitzovskost vzhledem k $x$. + Bez újmy na obecnosti nechť $t_0 > t$. Vezměme $(t; t_0, x_0) \in G$, buď $x$ maximální řešení s počáteční podmínkou $x(t_0) = x_0$. Pak $[t_0, t] \subset D_x$ (řešení je definováno na celém tomto intervalu). Vezměme $\delta > 0$ tak malé, aby $[t_0, t + 2\delta] \subset D_x$ (to můžeme, neboť $D_x$ je otevřená) a zároveň $K_\delta := \{ (y, s) \in \mathbb{R}^n \times \mathbb{R} : s \in [t_0 - \delta, t + \delta] \land |y(s) - x(s)| \leq \delta \} \subset \Omega$. Takto definovaná množina $K_\delta$ je kompaktní a tedy $f$ je na $K_\delta$ omezená konstantou $c_0$ (spojitá funkce na kompaktu) díky čemuž z lokální lipschitzovskosti plyne globální $L$-lipschitzovskost vzhledem k $x$. Dokážeme, že řešení ``blízko" toho původního neopustí ``rouru" $K_\delta$. Zvolme $\varepsilon > 0$ takové, aby $\varepsilon < \frac{\delta}{2(1 + c_0)e^{L(t - t_0 + 2\delta)}}$. Vezměme $y_0, s_0$ tak, aby $|s_0 - t_0| < \varepsilon$, $|x_0 - y_0| < \varepsilon$. Dále vezmeme $y$ maximální řešení s podmínkou $y(s_0) = y_0$. Chceme dokázat, že $y$ je definované aspoň na intervalu $[s_0, t + \delta]$ a platí $|y(s) - x(s)| \leq \delta$ pro všechna $s \in [s_0, t + \delta]$. Můžeme psát $$ |y(s_0) - x(s_0)| \leq |y(s_0) - x(t_0)| + |x(t_0) - x(s_0)| \leq $$ - $$ |y_0 - x_0| + |x'(\xi)| |t_0 - s_0| \leq (1 + C_0) \varepsilon, $$ + $$ |y_0 - x_0| + |x'(\xi)| |t_0 - s_0| \leq (1 + c_0) \varepsilon, $$ kde $\xi$ je konstanta z Lagrangeovy věty, která ve vícerozměrném prostoru platí pouze jako neostrá nerovnost. Dále odhadujme (použijeme Lemma \ref{lemma-sol-dist}) - $$ |y(s) - x(s)| \leq |y(s_0) - x(s_0)| e^{L|s - s_0|} \leq (1 + C_0) \varepsilon e^{L|s - s_0|} \leq (1+C_0)\varepsilon e^{L(t - t_0 + 2\delta)}, $$ + $$ |y(s) - x(s)| \leq |y(s_0) - x(s_0)| e^{L|s - s_0|} \leq (1 + c_0) \varepsilon e^{L|s - s_0|} \leq (1+c_0)\varepsilon e^{L(t - t_0 + 2\delta)}, $$ kde uvažujeme pouze body $s$, pro které existuje $y(s)$ a $y$ leží v $K_\delta$ na $[s_0, s]$. Z volby $\varepsilon$ dostáváme navíc \begin{equation} \label{eq-estimate-thm-sol-fun} - |y(s) - x(s)| \leq (1 + C_0) \varepsilon e^{L(t - t_0 + 2\delta} < \frac{\delta}{0}. + |y(s) - x(s)| \leq (1 + c_0) \varepsilon e^{L(t - t_0 + 2\delta)} < \frac{\delta}{2}. \end{equation} Maximální řešení $y$ opustí kompakt (Věta \ref{thm-leaving-compact}) $K_\delta$ někde za časem $s_0$. Označme $\gamma$ čas prvního opuštění (přesněji řečeno infimum všech časů, kdy to už není v tom kompaktu). Na intervalu $[s_0, \gamma]$ platí odhad \eqref{eq-estimate-thm-sol-fun}, tedy $|y(\gamma) - x(\gamma)| < \frac{\delta}{2}$, z čehož máme $\gamma = t + \delta$, to znamená, že kompakt nemůžeme opustit jinak než za časem $t$. Tím jsme dokázali otevřenost $G$. @@ -72,7 +72,7 @@ Například, uvažujeme-li rovnici $x'(t) = x(t)$. Obecným řešením této rov Dokážeme spojitost $\varphi$ na $G$. Vezměme dva body $(t; t_0, x_0)$ a $(s; s_0, y_0)$ jako minule a uvažujme rozdíl $$ | \varphi(t;t_0, x_0) - \varphi(s, s_0, y_0) | \leq |\varphi(t; t_0, x_0) - \varphi(s; t_0, x_0)| + $$ $$|\varphi(s; t_0, x_0) - \varphi(s; s_0, y_0)| \leq |x(t) - x(s)| + |x(s) - y(s)| \leq $$ - $$ C_0(t - s) + |x(s_0) - y(s_0)e^{L|s - s_0|}| \leq C_0|t - s| + (1 + C_0)e^{L|s - s_0|} |x_0 - y_0|,$$ + $$ c_0(t - s) + |x(s_0) - y(s_0)e^{L|s - s_0|}| \leq c_0|t - s| + (1 + c_0)e^{L|s - s_0|} |x_0 - y_0|,$$ čímž jsme ukázali lipschitzovskost, a tedy spojitost $\varphi$ na $G$. \end{proof}