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<b>thus </b><a NAME="E1:85"/>
<span class="p1">(<span class="default"><a href="borsuk_6.html#NK9" target="_self">IAA</a>  <a href="subset_1.html#K4">\/</a> <a href="borsuk_6.html#NK11" target="_self">IBB</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <a href="borsuk_6.html#NK13" target="_self">ICC</a>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span><a href="mcart_1.html#K12">:]</a></span>
 <b>by </b><i><a class="ref" href="borsuk_6.html#T1" target="_self">Th1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>let </b><font color="Maroon">c<sub>1</sub></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="E2:85"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span><a href="mcart_1.html#K12">:]</a></span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="mcart_1.html#K1">`1</a> , <font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="mcart_1.html#K2">`2</a>  as   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a>  <b>by </b><i><a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a>, <a class="ref" href="mcart_1.html#T10">MCART_1:10</a></i>;<br/>
<a NAME="E4:85"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<b>by </b><i><a class="txt" href="borsuk_6.html#E2:85"><i><font color="Green">E64</font></i></a>, <a class="ref" href="mcart_1.html#T23">MCART_1:23</a></i>;<br/>
<a NAME="E5:85"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK9" target="_self">IAA</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK11" target="_self">IBB</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK13" target="_self">ICC</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:85_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> or <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_1_1_1"><b>suppose </b></a><a NAME="E1:85_1_1_1"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:85_1_1_1_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 or <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:85_1_1_1_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:85_1_1_1_1_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK9" target="_self">IAA</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK11" target="_self">IBB</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK13" target="_self">ICC</a>  )
 <b>by </b><i><a class="txt" href="borsuk_6.html#E4:85"><i><font color="Green">E65</font></i></a>, <a class="txt" href="borsuk_6.html#E1:85_1_1_1"><i><font color="Green">E66</font></i></a>, <a class="ref" href="borsuk_6.html#D11" target="_self">Def11</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:85_1_1_1_1_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:85_1_1_1_1_1_2"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK9" target="_self">IAA</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK11" target="_self">IBB</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK13" target="_self">ICC</a>  )
 <b>by </b><i><a class="txt" href="borsuk_6.html#E4:85"><i><font color="Green">E65</font></i></a>, <a class="ref" href="borsuk_6.html#D12" target="_self">Def12</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:85_1_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK9" target="_self">IAA</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK11" target="_self">IBB</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK13" target="_self">ICC</a>  )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_1_1_2"><b>suppose </b></a><a NAME="E1:85_1_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:85_1_1_2"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK9" target="_self">IAA</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK11" target="_self">IBB</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK13" target="_self">ICC</a>  )
 <b>by </b><i><a class="txt" href="borsuk_6.html#E4:85"><i><font color="Green">E65</font></i></a>, <a class="ref" href="borsuk_6.html#D10" target="_self">Def10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E6:85"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <a href="borsuk_6.html#NK9" target="_self">IAA</a>  <a href="subset_1.html#K4">\/</a> <a href="borsuk_6.html#NK11" target="_self">IBB</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK13" target="_self">ICC</a>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E7:85"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="borsuk_6.html#NK9" target="_self">IAA</a>  <a href="subset_1.html#K4">\/</a> <a href="borsuk_6.html#NK11" target="_self">IBB</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <a href="borsuk_6.html#NK13" target="_self">ICC</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


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