<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">XX</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="borsuk_1.html#V1" target="_self">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">XX</font>;<br/><b>let </b><font color="Maroon">D</font> be   <a href="borsuk_1.html#NM2">DECOMPOSITION</a> of <font color="Maroon">X</font>;<br/>





<a NAME="E1:110"/>
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><font color="Maroon">XX</font>,<a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="borsuk_1.html#K5" target="_self">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">XX</font>,the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="zfmisc_1.html#K2">:]</a></span> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span>,<a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="borsuk_1.html#K5" target="_self">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">II</font> = <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_1.html#K20" target="_self">I[01]</a> </span>)</span></span><a href="funct_3.html#K16">:]</a></span> as   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><font color="Maroon">XX</font>,<a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="borsuk_1.html#K5" target="_self">:]</a></span>,the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span>,<a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="borsuk_1.html#K5" target="_self">:]</a></span> ;<br/>
<b>given </b><font color="Maroon">CH1</font> being  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><font color="Maroon">XX</font>,<a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="borsuk_1.html#K5" target="_self">:]</a></span>,<font color="Maroon">XX</font><b> such that </b><a NAME="E3:110"/><i><font color="Green">E24</font></i>: 
for <font color="Olive">A</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">XX</font> holds <br/> ( <font color="Maroon">CH1</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Olive">A</font>,<a href="borsuk_1.html#K21" target="_self">0[01]</a> </span><a href="borsuk_1.html#K7" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <font color="Olive">A</font> &amp; <font color="Maroon">CH1</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Olive">A</font>,<a href="borsuk_1.html#K22" target="_self">1[01]</a> </span><a href="borsuk_1.html#K7" target="_self">]</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font> &amp; ( <font color="Olive">A</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font> implies for <font color="Olive">T</font> being  <a href="pre_topc.html#NM2">Point</a> of <a href="borsuk_1.html#K20" target="_self">I[01]</a>  holds  <font color="Maroon">CH1</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Olive">A</font>,<font color="Olive">T</font></span><a href="borsuk_1.html#K7" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <font color="Olive">A</font> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_1.html#D21" target="_self">BORSUK_1:def 21</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="110_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">xx</font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><font color="Maroon">XX</font>,<a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="borsuk_1.html#K5" target="_self">:]</a></span>, <font color="Maroon">xx'</font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><font color="Maroon">XX</font>,<a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="borsuk_1.html#K5" target="_self">:]</a></span><b> such that </b><a NAME="E1:110_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">II</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx</font> <a href="hidden.html#R1">=</a> <font color="Maroon">II</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx'</font>
 <b>and </b><br/><a NAME="E2:110_1"/><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">CH1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">CH1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx'</font>
 ;<br/><b>consider </b><font color="Maroon">x</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">XX</font>, <font color="Maroon">t</font> being   <a href="pre_topc.html#NM2">Point</a> of <a href="borsuk_1.html#K20" target="_self">I[01]</a> <b> such that </b><br/><a NAME="E4:110_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">xx</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">t</font></span><a href="borsuk_1.html#K7" target="_self">]</a></span>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">x'</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">XX</font>, <font color="Maroon">t'</font> being   <a href="pre_topc.html#NM2">Point</a> of <a href="borsuk_1.html#K20" target="_self">I[01]</a> <b> such that </b><br/><a NAME="E6:110_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">xx'</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">x'</font>,<font color="Maroon">t'</font></span><a href="borsuk_1.html#K7" target="_self">]</a></span>
 <b>by </b><i/>;<br/><a NAME="E7:110_1"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">II</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">x</font>,<font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p4">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>,<font color="Maroon">t</font></span><a href="borsuk_1.html#K7" target="_self">]</a></span> &amp; <font color="Maroon">II</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">x'</font>,<font color="Maroon">t'</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p4">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x'</font></span>)</span>,<font color="Maroon">t'</font></span><a href="borsuk_1.html#K7" target="_self">]</a></span> )
 <b>by </b><i/>;<br/><a NAME="E8:110_1"/><b>then </b>
( <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t'</font> &amp; <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x'</font> )
 <b>by </b><i><a class="ref" href="borsuk_1.html#T31" target="_self">Th31</a>, <a class="ref" href="borsuk_1.html#T32" target="_self">Th32</a>, <a class="ref" href="borsuk_1.html#T29" target="_self">Th29</a>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><a NAME="E9:110_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font> &amp; <font color="Maroon">x'</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font> )
 <b>by </b><i><a class="ref" href="borsuk_1.html#T30" target="_self">Th30</a>, <a class="ref" href="borsuk_1.html#T31" target="_self">Th31</a>, <a class="ref" href="borsuk_1.html#T32" target="_self">Th32</a>, </i>;<br/><a NAME="E10:110_1"/><b>then </b><i><font color="Green">E36</font></i>: 
( <font color="Maroon">CH1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">CH1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x'</font> )
 <b>by </b><i>, <a class="ref" href="borsuk_1.html#T31" target="_self">Th31</a>, <a class="ref" href="borsuk_1.html#T32" target="_self">Th32</a></i>;<br/><a NAME="E11:110_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">CH1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">CH1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">CH1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">CH1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx'</font></span>)</span> )
 <b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>;<br/><b>hence </b><a NAME="E12:110_1"/>
contradiction
 <b>by </b><i><a class="ref" href="borsuk_1.html#T29" target="_self">Th29</a>, <a class="ref" href="borsuk_1.html#T30" target="_self">Th30</a>, , , <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a>, <a class="ref" href="borsuk_1.html#T31" target="_self">Th31</a>, <a class="ref" href="borsuk_1.html#T32" target="_self">Th32</a></i>;<br/></div><b>end;</b></div>
<b>then consider </b><font color="Maroon">THETA</font> being   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span>,<a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="borsuk_1.html#K5" target="_self">:]</a></span>,the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span><b> such that </b><br/><a NAME="E6:110"/><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">CH1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">THETA</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">II</font>
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">THETA</font> = <font color="Maroon">THETA</font> as   <a href="struct_0.html#NM6">Function</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span>,<a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="borsuk_1.html#K5" target="_self">:]</a></span>,<span class="p1">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> ;<br/>
<a NAME="E8:110"/>
<font color="Maroon">THETA</font> is <a href="pre_topc.html#V5">continuous</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="110_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">WT</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span>,<a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="borsuk_1.html#K5" target="_self">:]</a></span>; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_1.html#D3" target="_self">BORSUK_1:def 3</a><br/>

<b>reconsider </b><font color="Maroon">xt'</font> = <font color="Maroon">WT</font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="zfmisc_1.html#K2">:]</a></span> <b>by </b><i/>;<br/>
<b>let </b><font color="Maroon">G</font> be    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">THETA</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">WT</font>;<br/>

<b>reconsider </b><font color="Maroon">FF</font> = <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">CH1</font> as  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><font color="Maroon">XX</font>,<a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="borsuk_1.html#K5" target="_self">:]</a></span>,<span class="p1">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="tops_2.html#T58">TOPS_2:58</a></i>;<br/>
<b>consider </b><font color="Maroon">W</font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span>, <font color="Maroon">T</font> being   <a href="pre_topc.html#NM2">Point</a> of <a href="borsuk_1.html#K20" target="_self">I[01]</a> <b> such that </b><br/><a NAME="E4:110_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">WT</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W</font>,<font color="Maroon">T</font></span><a href="borsuk_1.html#K7" target="_self">]</a></span>
 <b>by </b><i><a class="txt" href="borsuk_1.html#E4:110_2"><i><font color="Green">E38</font></i></a></i>;<br/>
<a NAME="E5:110_2"/>
<font color="Maroon">II</font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">xt'</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K6" target="_self">[:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p4">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">W</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">T</font></span><a href="domain_1.html#K6">}</a></span></span><a href="borsuk_1.html#K6" target="_self">:]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T30" target="_self">Th30</a>, </i>;<br/>
<a NAME="E6:110_2"/><b>then </b>
<span class="p1"><a href="borsuk_1.html#K6" target="_self">[:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p4">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">W</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">T</font></span><a href="domain_1.html#K6">}</a></span></span><a href="borsuk_1.html#K6" target="_self">:]</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">FF</font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">THETA</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">WT</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T29" target="_self">Th29</a>, </i>;<br/>
<b>then reconsider </b><font color="Maroon">GG</font> = <font color="Maroon">FF</font> <a href="borsuk_1.html#K4" target="_self">"</a> <font color="Maroon">G</font> as    <a href="connsp_2.html#M2">a_neighborhood</a> of <span class="p1"><a href="borsuk_1.html#K6" target="_self">[:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p4">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">W</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">T</font></span><a href="domain_1.html#K6">}</a></span></span><a href="borsuk_1.html#K6" target="_self">:]</a></span> <b>by </b><i/>;<br/>
<a NAME="E8:110_2"/>
<font color="Maroon">W</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E9:110_2"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">W</font> <a href="hidden.html#R2">in</a>  <a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font>
 
<b>by </b><i/>;<br/>
<a NAME="E10:110_2"/>
<span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">W</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T31" target="_self">Th31</a>, <a class="ref" href="borsuk_1.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E11:110_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">W</font></span><a href="domain_1.html#K6">}</a></span> is <a href="compts_1.html#V6">compact</a>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T31" target="_self">Th31</a>, <a class="ref" href="borsuk_1.html#T26" target="_self">Th26</a></i>;<br/>
<b>then consider </b><font color="Maroon">U</font> being    <a href="connsp_2.html#M2">a_neighborhood</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">W</font></span><a href="domain_1.html#K6">}</a></span>, <font color="Maroon">V</font> being    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E13:110_2"/><i><font color="Green">E40</font></i>: 
<span class="p1"><a href="borsuk_1.html#K9" target="_self">[:</a><span class="default"><font color="Maroon">U</font>,<font color="Maroon">V</font></span><a href="borsuk_1.html#K9" target="_self">:]</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">GG</font>
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">H'</font> = <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">U</font> as    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">W</font> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">H''</font> = <span class="p1"><a href="borsuk_1.html#K8" target="_self">[:</a><span class="default"><font color="Maroon">H'</font>,<font color="Maroon">V</font></span><a href="borsuk_1.html#K8" target="_self">:]</a></span> as    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">WT</font> <b>by </b><i><a class="ref" href="borsuk_1.html#T30" target="_self">Th30</a></i>;<br/>
<b>take </b><font color="Maroon">H</font> = <font color="Maroon">H''</font>;<br/>

<a NAME="E16:110_2"/><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">CH1</font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">GG</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T145">FUNCT_1:145</a></i>;<br/>
<a NAME="E17:110_2"/>
<font color="Maroon">II</font> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="borsuk_1.html#K9" target="_self">[:</a><span class="default"><font color="Maroon">U</font>,<font color="Maroon">V</font></span><a href="borsuk_1.html#K9" target="_self">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K6" target="_self">[:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p4">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">U</font></span>)</span>,<font color="Maroon">V</font></span><a href="borsuk_1.html#K6" target="_self">:]</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E18:110_2"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">THETA</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">CH1</font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="borsuk_1.html#K9" target="_self">[:</a><span class="default"><font color="Maroon">U</font>,<font color="Maroon">V</font></span><a href="borsuk_1.html#K9" target="_self">:]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T29" target="_self">Th29</a>, <a class="ref" href="relat_1.html#T159">RELAT_1:159</a></i>;<br/>
<a NAME="E19:110_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">CH1</font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="borsuk_1.html#K9" target="_self">[:</a><span class="default"><font color="Maroon">U</font>,<font color="Maroon">V</font></span><a href="borsuk_1.html#K9" target="_self">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">CH1</font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">GG</font>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T32" target="_self">Th32</a>, <a class="ref" href="relat_1.html#T156">RELAT_1:156</a></i>;<br/>
<b>hence </b><a NAME="E20:110_2"/>
<font color="Maroon">THETA</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">H</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font>
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">THETA'</font> = <font color="Maroon">THETA</font> as  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p3">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span>,<a href="borsuk_1.html#K20" target="_self">I[01]</a> </span><a href="borsuk_1.html#K5" target="_self">:]</a></span>,<span class="p1">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> ;<br/>
<b>take </b><font color="Maroon">THETA''</font> = <font color="Maroon">THETA'</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_1.html#D21" target="_self">BORSUK_1:def 21</a><br/>

<b>let </b><font color="Maroon">W</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span>;<br/>

<b>consider </b><font color="Maroon">W'</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">XX</font><b> such that </b><br/><a NAME="E11:110"/><i><font color="Green">E43</font></i>: 
<span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">W'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font>
 <b>by </b><i/>;<br/>
<a NAME="E12:110"/>
( <font color="Maroon">CH1</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">W'</font>,<a href="borsuk_1.html#K21" target="_self">0[01]</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W'</font> &amp; <font color="Maroon">II</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">W'</font>,<a href="borsuk_1.html#K21" target="_self">0[01]</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W</font>,<a href="borsuk_1.html#K21" target="_self">0[01]</a> </span><a href="borsuk_1.html#K7" target="_self">]</a></span> )
 
<b>by </b><i>, <a class="ref" href="borsuk_1.html#T30" target="_self">Th30</a>, </i>;<br/>
<a NAME="E13:110"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">THETA'</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">II</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W'</font>,<a href="borsuk_1.html#K21" target="_self">0[01]</a> </span><a href="borsuk_1.html#K7" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">THETA'</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W</font>,<a href="borsuk_1.html#K21" target="_self">0[01]</a> </span><a href="borsuk_1.html#K7" target="_self">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">THETA'</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">II</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W'</font>,<a href="borsuk_1.html#K21" target="_self">0[01]</a> </span><a href="borsuk_1.html#K7" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> )
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T29" target="_self">Th29</a>, <a class="ref" href="borsuk_1.html#T30" target="_self">Th30</a>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>;<br/>
<b>hence </b><a NAME="E14:110"/>
<font color="Maroon">THETA''</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W</font>,<a href="borsuk_1.html#K21" target="_self">0[01]</a> </span><a href="borsuk_1.html#K7" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font>
 ;<br/>

<a NAME="E15:110"/>
<font color="Maroon">II</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">W'</font>,<a href="borsuk_1.html#K22" target="_self">1[01]</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W</font>,<a href="borsuk_1.html#K22" target="_self">1[01]</a> </span><a href="borsuk_1.html#K7" target="_self">]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T30" target="_self">Th30</a>, </i>;<br/>
<a NAME="E16:110"/><b>then </b><i><font color="Green">E44</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">THETA'</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">II</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W'</font>,<a href="borsuk_1.html#K22" target="_self">1[01]</a> </span><a href="borsuk_1.html#K7" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">THETA'</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W</font>,<a href="borsuk_1.html#K22" target="_self">1[01]</a> </span><a href="borsuk_1.html#K7" target="_self">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">THETA'</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">II</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W'</font>,<a href="borsuk_1.html#K22" target="_self">1[01]</a> </span><a href="borsuk_1.html#K7" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K18" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">CH1</font> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W'</font>,<a href="borsuk_1.html#K22" target="_self">1[01]</a> </span><a href="borsuk_1.html#K7" target="_self">]</a></span></span>)</span> )
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T29" target="_self">Th29</a>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>;<br/>
<a NAME="E17:110"/>
<font color="Maroon">CH1</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W'</font>,<a href="borsuk_1.html#K22" target="_self">1[01]</a> </span><a href="borsuk_1.html#K7" target="_self">]</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E18:110"/>
<font color="Maroon">THETA''</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W</font>,<a href="borsuk_1.html#K22" target="_self">1[01]</a> </span><a href="borsuk_1.html#K7" target="_self">]</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K19" target="_self">space</a> <font color="Maroon">D</font></span>)</span>
 <b>by </b><i><a class="ref" href="borsuk_1.html#T31" target="_self">Th31</a>, <a class="ref" href="borsuk_1.html#T20" target="_self">Th20</a></i>;<br/>

<b>assume </b><a NAME="E19:110"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">W</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K19" target="_self">space</a> <font color="Maroon">D</font></span>)</span>
 ;<br/>

<b>let </b><font color="Maroon">T</font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="borsuk_1.html#K20" target="_self">I[01]</a> ;<br/>

<a NAME="E20:110"/>
<font color="Maroon">W'</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T30" target="_self">Th30</a>, <a class="ref" href="borsuk_1.html#T32" target="_self">Th32</a>, </i>;<br/>
<a NAME="E21:110"/><b>then </b>
( <font color="Maroon">CH1</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">W'</font>,<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W'</font> &amp; <font color="Maroon">II</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">W'</font>,<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W</font>,<font color="Maroon">T</font></span><a href="borsuk_1.html#K7" target="_self">]</a></span> )
 
<b>by </b><i>, <a class="ref" href="borsuk_1.html#T30" target="_self">Th30</a>, </i>;<br/>
<a NAME="E22:110"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">THETA'</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">II</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W'</font>,<font color="Maroon">T</font></span><a href="borsuk_1.html#K7" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">THETA'</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W</font>,<font color="Maroon">T</font></span><a href="borsuk_1.html#K7" target="_self">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">THETA'</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">II</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W'</font>,<font color="Maroon">T</font></span><a href="borsuk_1.html#K7" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> )
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T29" target="_self">Th29</a>, <a class="ref" href="borsuk_1.html#T30" target="_self">Th30</a>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>;<br/>
<b>hence </b><a NAME="E23:110"/>
<font color="Maroon">THETA''</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7" target="_self">[</a><span class="default"><font color="Maroon">W</font>,<font color="Maroon">T</font></span><a href="borsuk_1.html#K7" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font>
 ;<br/>


</div>
