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<b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">c</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">d</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:45"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">c</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">d</font> )
 ;<br/>

<a NAME="E2:45"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></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/>
<a NAME="E3:45"/><b>then </b>
<font color="Maroon">a</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="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="topmetr.html#T25">TOPMETR:25</a></i>;<br/>
<a NAME="E4:45"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4">P[01]</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span>,<span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="borsuk_6.html#K1" target="_self">L[01]</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="treal_1.html#K4">P[01]</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span>,<span class="p3">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="treal_1.html#K4">P[01]</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span>,<span class="p3">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="treal_1.html#D1">TREAL_1:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="treal_1.html#K2">(#)</a> </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#T16">TREAL_1:16</a></i>
<br/>.= 
 <a href="treal_1.html#K1">(#)</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
<b>by </b><i>, <a class="ref" href="treal_1.html#T12">TREAL_1:12</a></i>
<br/>.= 
<font color="Maroon">c</font>
<b>by </b><i>, <a class="ref" href="treal_1.html#D1">TREAL_1:def 1</a></i>
;<br/>

<a NAME="E6:45"/>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></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/>
<a NAME="E7:45"/><b>then </b>
<font color="Maroon">b</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="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="topmetr.html#T25">TOPMETR:25</a></i>;<br/>
<a NAME="E8:45"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4">P[01]</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span>,<span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="borsuk_6.html#K1" target="_self">L[01]</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> = 
<span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="treal_1.html#K4">P[01]</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span>,<span class="p3">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="treal_1.html#K4">P[01]</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><a href="treal_1.html#K1">(#)</a> 0,1</span>)</span>,<span class="p3">(<span class="default">0,1 <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="treal_1.html#K2">(#)</a> </span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="treal_1.html#D2">TREAL_1:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="treal_1.html#K3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="treal_1.html#K2">(#)</a> </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#T16">TREAL_1:16</a></i>
<br/>.= 
<font color="Maroon">c</font>,<font color="Maroon">d</font> <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/>.= 
<font color="Maroon">d</font>
<b>by </b><i>, <a class="ref" href="treal_1.html#D2">TREAL_1:def 2</a></i>
;<br/>


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