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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>, <font color="Maroon">b</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">P</font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:52"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>and </b><br/><a NAME="E2:52"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/>

<b>set </b><font color="Maroon">e</font> =  <a href="treal_1.html#K3">L[01]</a> <span class="p1">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span>;<br/>
<i><font color="Green">E34</font></i>: <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 0 = 
<span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span>
<b>by </b><i><a class="ref" href="treal_1.html#D1">TREAL_1:def 1</a></i>
<br/>.= 
0,1 <a href="treal_1.html#K2">(#)</a> 
<b>by </b><i><a class="ref" href="treal_1.html#T12">TREAL_1:12</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="treal_1.html#D2">TREAL_1:def 2</a></i>
;<br/>
<i><font color="Green">E35</font></i>: <span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 = 
<span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span>
<b>by </b><i><a class="ref" href="treal_1.html#D2">TREAL_1:def 2</a></i>
<br/>.= 
 <a href="treal_1.html#K1">(#)</a> 0,1
<b>by </b><i><a class="ref" href="treal_1.html#T12">TREAL_1:12</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="treal_1.html#D1">TREAL_1:def 1</a></i>
;<br/>
<a NAME="E5:52"/><i><font color="Green">E36</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span>
 
<b>by </b><i><a class="ref" href="topmetr.html#T25">TOPMETR:25</a></i>;<br/>
<a NAME="E6:52"/>
0 <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T48">RCOMP_1:48</a></i>;<br/>
<b>hence </b><a NAME="E7:52"/>
<span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p3">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span>,<span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i>, , <a class="ref" href="borsuk_6.html#T6" target="_self">Th6</a>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>;<br/>

<a NAME="E8:52"/>
1 <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T48">RCOMP_1:48</a></i>;<br/>
<b>hence </b><a NAME="E9:52"/>
<span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p3">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span>,<span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="borsuk_6.html#T5" target="_self">Th5</a>, <a class="ref" href="borsuk_6.html#T6" target="_self">Th6</a>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>;<br/>


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