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<b>thus </b><a NAME="E1:101"/>
<a href="borsuk_6.html#NK9" target="_self">IAA</a>  <a href="subset_1.html#K9">/\</a> <a href="borsuk_6.html#NK13" target="_self">ICC</a>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,0</span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_1"><b>proof </b></a><div class="add">

<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="E1:101_1"/><i><font color="Green">E80</font></i>: 
<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#K9">/\</a> <a href="borsuk_6.html#NK13" target="_self">ICC</a> 
 ;<br/>

<a NAME="E2:101_1"/><b>then </b><i><font color="Green">E81</font></i>: 
( <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>  &amp; <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#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><a href="topmetr.html#K5">I[01]</a> ,<a href="topmetr.html#K5">I[01]</a> </span><a href="borsuk_1.html#K5">:]</a></span> <b>by </b><i><a class="txt" href="borsuk_6.html#E1:101_1"><i><font color="Green">E80</font></i></a></i>;<br/>
<a NAME="E4:101_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><a href="topmetr.html#K5">I[01]</a> ,<a href="topmetr.html#K5">I[01]</a> </span><a href="borsuk_1.html#K5">:]</a></span>
 
;<br/>
<a NAME="E5:101_1"/><b>then </b><i><font color="Green">E82</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> ,the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> </span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#D5">BORSUK_1:def 5</a></i>;<br/>
<a NAME="E6:101_1"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="mcart_1.html#K1">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="real_1.html#K6">/</a> 2
 
<b>by </b><i><a class="txt" href="borsuk_6.html#E2:101_1"><i><font color="Green">E81</font></i></a>, <a class="ref" href="borsuk_6.html#T68" target="_self">Th68</a></i>;<br/>
<a NAME="E7:101_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="mcart_1.html#K1">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K6">/</a> 2
 
<b>by </b><i><a class="txt" href="borsuk_6.html#E2:101_1"><i><font color="Green">E81</font></i></a>, <a class="ref" href="borsuk_6.html#T67" target="_self">Th67</a></i>;<br/>
<a NAME="E8:101_1"/><b>then </b><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K6">/</a> 2
 
<b>by </b><i><a class="txt" href="borsuk_6.html#E6:101_1"><i><font color="Green">E83</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><a href="topmetr.html#K5">I[01]</a> ,<a href="topmetr.html#K5">I[01]</a> </span><a href="borsuk_1.html#K5">:]</a></span><b> such that </b><br/><a NAME="E10:101_1"/><i><font color="Green">E85</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="mcart_1.html#K2">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="mcart_1.html#K1">`1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 )
 <b>by </b><i><a class="txt" href="borsuk_6.html#E2:101_1"><i><font color="Green">E81</font></i></a>, <a class="ref" href="borsuk_6.html#T63" target="_self">Th63</a></i>;<br/>
<a NAME="E11:101_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="mcart_1.html#K2">`2</a>  is   <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_6.html#T31" target="_self">Th31</a></i>;<br/>
<a NAME="E12:101_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="borsuk_6.html#E8:101_1"><i><font color="Green">E84</font></i></a>, <a class="txt" href="borsuk_6.html#E10:101_1"><i><font color="Green">E85</font></i></a>, <a class="ref" href="borsuk_1.html#T86">BORSUK_1:86</a></i>;<br/>
<a NAME="E13:101_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,0</span><a href="tarski.html#K4">]</a></span>
 
<b>by </b><i><a class="txt" href="borsuk_6.html#E5:101_1"><i><font color="Green">E82</font></i></a>, <a class="txt" href="borsuk_6.html#E8:101_1"><i><font color="Green">E84</font></i></a>, <a class="ref" href="mcart_1.html#T23">MCART_1:23</a></i>;<br/>
<b>hence </b><a NAME="E14:101_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,0</span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div><b>end;</b></div>

<a NAME="E2:101"/><i><font color="Green">E80</font></i>: 
1 <a href="real_1.html#K6">/</a> 2 is   <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#T86">BORSUK_1:86</a></i>;<br/>
<a NAME="E3:101"/><b>then </b><i><font color="Green">E81</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,0</span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="borsuk_6.html#NK9" target="_self">IAA</a> 
 
<b>by </b><i><a class="ref" href="borsuk_6.html#T78" target="_self">Th78</a></i>;<br/>
<a NAME="E4:101"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,0</span><a href="tarski.html#K4">]</a></span> <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#E2:101"><i><font color="Green">E80</font></i></a>, <a class="ref" href="borsuk_6.html#T77" target="_self">Th77</a></i>;<br/>
<a NAME="E5:101"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,0</span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <a href="borsuk_6.html#NK9" target="_self">IAA</a>  <a href="subset_1.html#K9">/\</a> <a href="borsuk_6.html#NK13" target="_self">ICC</a> 
 
<b>by </b><i><a class="txt" href="borsuk_6.html#E3:101"><i><font color="Green">E81</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:101"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,0</span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <a href="borsuk_6.html#NK9" target="_self">IAA</a>  <a href="subset_1.html#K9">/\</a> <a href="borsuk_6.html#NK13" target="_self">ICC</a> 
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>


</div>
