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<span class="kw">let </span><font color="Maroon" title="c1">s</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<font color="Maroon" title="c1">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="borsuk_6.html#NK11" title="BORSUK_6:NK.11">IBB</a>  implies <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/>

<span class="kw">assume </span><a NAME="E1:87"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<font color="Maroon" title="c1">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="borsuk_6.html#NK11" title="BORSUK_6:NK.11">IBB</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a><span class="kw"> such that </span><br/><a NAME="E3:87"/><span class="lab"><font color="Green" title="E66">A1</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<font color="Maroon" title="c1">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E4:87"/><span class="lab"><font color="Green" title="E67">A2</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">a</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:87"/>
<font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_6.html#D9" target="_self" title="BORSUK_6:def.9">Def11</a></span>;<br/>
<a NAME="E6:87"/><span class="lab"><font color="Green" title="E68">A3</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T43" title="BORSUK_1:th.43">BORSUK_1:43</a></span>;<br/>
<a NAME="E7:87"/>
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E66">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:87"/>
<font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:87"><span class="lab"><font color="Green" title="E67">A2</font></span></a>, <a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E68">A3</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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