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<b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="borsuk_1.html#K20">I[01]</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="borsuk_1.html#K20">I[01]</a> ;<br/>



<b>assume </b><a NAME="E1:2"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,1</span><a href="rcomp_2.html#K2">.]</a></span>
 ;<br/>

<b>set </b><font color="Maroon">I</font> = the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_1.html#K20">I[01]</a> ;<br/>
<b>set </b><font color="Maroon">Y</font> = <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,<font color="Maroon">a</font></span><a href="rcomp_1.html#K1">.]</a></span>;<br/>
<a NAME="E2:2"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">X</font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_1.html#K20">I[01]</a>  <a href="subset_1.html#K6">\</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="subset_1.html#D5">SUBSET_1:def 5</a></i>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:2_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="subset_1.html#K3">`</a> 
 ;<br/><b>then reconsider </b><font color="Maroon">y</font> = <font color="Maroon">x</font> as   <a href="pre_topc.html#NM2">Point</a> of <a href="borsuk_1.html#K20">I[01]</a>  ;<br/><a NAME="E3:2_1"/><i><font color="Green">E48</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="jordan5a.html#T2">JORDAN5A:2</a></i>;<br/><a NAME="E4:2_1"/>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E5:2_1"/><b>then </b>
( <font color="Maroon">y</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a</font> or <font color="Maroon">y</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 )
 <b>by </b><i>, <a class="ref" href="rcomp_2.html#T4">RCOMP_2:4</a></i>;<br/><b>hence </b><a NAME="E6:2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,<font color="Maroon">a</font></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i>, <a class="ref" href="jordan5a.html#T2">JORDAN5A:2</a>, <a class="ref" href="rcomp_1.html#T48">RCOMP_1:48</a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E4:2"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,<font color="Maroon">a</font></span><a href="rcomp_1.html#K1">.]</a></span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">y</font> = <font color="Maroon">x</font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E6:2"/><i><font color="Green">E50</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">y</font>
 
<b>by </b><i>, <a class="ref" href="rcomp_1.html#T48">RCOMP_1:48</a></i>;<br/>
<a NAME="E7:2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">y</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a</font>
 
<b>by </b><i>, <a class="ref" href="rcomp_1.html#T48">RCOMP_1:48</a></i>;<br/>
<a NAME="E8:2"/>
<font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 
<b>by </b><i><a class="ref" href="jordan5a.html#T2">JORDAN5A:2</a></i>;<br/>
<a NAME="E9:2"/><b>then </b>
<font color="Maroon">y</font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E10:2"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_1.html#K20">I[01]</a> 
 
<b>by </b><i>, <a class="ref" href="jordan5a.html#T2">JORDAN5A:2</a></i>;<br/>
<a NAME="E11:2"/>
not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
<b>by </b><i>, , <a class="ref" href="rcomp_2.html#T4">RCOMP_2:4</a></i>;<br/>
<b>hence </b><a NAME="E12:2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>


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