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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></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="E1:94"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:94"/><b>then </b><i><font color="Green">E78</font></i>: 
not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="borsuk_5.html#NK4" target="_self">].</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_5.html#NK4" target="_self">,+infty.[</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T86" target="_self">Th86</a></i>;<br/>
<a NAME="E3:94"/>
not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="borsuk_5.html#NK4" target="_self">].</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_5.html#NK4" target="_self">,+infty.[</a></span>
 
<b>by </b><i><a class="txt" href="borsuk_5.html#E1:94"><i><font color="Green">E77</font></i></a>, <a class="ref" href="borsuk_5.html#T87" target="_self">Th87</a></i>;<br/>
<a NAME="E4:94"/><b>then </b><i><font color="Green">E79</font></i>: 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="borsuk_5.html#NK4" target="_self">].</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_5.html#NK4" target="_self">,+infty.[</a></span>
 
<b>by </b><i><a class="txt" href="borsuk_5.html#E2:94"><i><font color="Green">E78</font></i></a>, <a class="ref" href="zfmisc_1.html#T57">ZFMISC_1:57</a></i>;<br/>
<span class="p1"><a href="borsuk_5.html#NK3" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="borsuk_5.html#NK3" target="_self">,+infty.[</a></span> = 
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="borsuk_5.html#NK3" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_5.html#NK3" target="_self">,+infty.[</a></span>
<b>by </b><i><a class="txt" href="borsuk_5.html#E1:94"><i><font color="Green">E77</font></i></a>, <a class="ref" href="borsuk_5.html#T28" target="_self">Th28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="borsuk_5.html#NK3" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_5.html#NK3" target="_self">,+infty.[</a></span>
<b>by </b><i><a class="txt" href="borsuk_5.html#E1:94"><i><font color="Green">E77</font></i></a>, <a class="ref" href="rcomp_1.html#T11">RCOMP_1:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="seq_4.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="borsuk_5.html#NK4" target="_self">].</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_5.html#NK4" target="_self">,+infty.[</a></span></span>)</span>
<b>by </b><i><a class="ref" href="borsuk_5.html#T67" target="_self">Th67</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="seq_4.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="borsuk_5.html#NK4" target="_self">].</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_5.html#NK4" target="_self">,+infty.[</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="seq_4.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="borsuk_5.html#NK4" target="_self">].</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_5.html#NK4" target="_self">,+infty.[</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="borsuk_5.html#NK4" target="_self">].</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_5.html#NK4" target="_self">,+infty.[</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T14">ZFMISC_1:14</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="borsuk_5.html#NK4" target="_self">].</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_5.html#NK4" target="_self">,+infty.[</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
;<br/>
<a NAME="E6:94"/><b>then </b>
<span class="p1"><a href="borsuk_5.html#NK3" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="borsuk_5.html#NK3" target="_self">,+infty.[</a></span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="borsuk_5.html#NK4" target="_self">].</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_5.html#NK4" target="_self">,+infty.[</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="txt" href="borsuk_5.html#E4:94"><i><font color="Green">E79</font></i></a>, <a class="ref" href="xboole_1.html#T88">XBOOLE_1:88</a></i>;<br/>
<b>hence </b><a NAME="E7:94"/>
<span class="p1"><a href="borsuk_5.html#NK3" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="borsuk_5.html#NK3" target="_self">,+infty.[</a></span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="borsuk_5.html#NK4" target="_self">].</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_5.html#NK4" target="_self">,+infty.[</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="seq_4.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="seq_4.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>;<br/>


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