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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="E1:63"/><i><font color="Green">E31</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 href="numbers.html#K1">REAL</a>  = 
<span class="p1">(<span class="default"><a href="numbers.html#K1">REAL</a>  <a href="subset_1.html#K6">\</a> <span class="p2"><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></span>)</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>1</sub></font></span><a href="seq_4.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T45">XBOOLE_1:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_5.html#NK2" target="_self">].-infty,</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="borsuk_5.html#NK4" target="_self">].</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</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>1</sub></font></span><a href="seq_4.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="borsuk_5.html#T18">BORSUK_5:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="borsuk_5.html#NK2" target="_self">].-infty,</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_5.html#NK4" target="_self">].</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><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></span>)</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"><a href="borsuk_5.html#NK2" target="_self">].-infty,</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="borsuk_5.html#NK3" target="_self">[.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="borsuk_5.html#T67">BORSUK_5:67</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="borsuk_5.html#NK2" target="_self">].-infty,</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2"><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="p2">(<span class="default"><a href="borsuk_5.html#NK3" target="_self">[.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="borsuk_5.html#T28">BORSUK_5:28</a>, <a class="txt" href="isomichi.html#E1:63"><i><font color="Green">E31</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="borsuk_5.html#NK2" target="_self">].-infty,</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2"><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="p2">(<span class="default"><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> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><a href="borsuk_5.html#NK4" target="_self">].</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="borsuk_5.html#T67">BORSUK_5:67</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="borsuk_5.html#NK2" target="_self">].-infty,</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><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="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="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="borsuk_5.html#NK4" target="_self">].</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</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"><a href="borsuk_5.html#NK2" target="_self">].-infty,</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><span class="p3"><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="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></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="borsuk_5.html#NK4" target="_self">].</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
;<br/>
<b>hence </b><a NAME="E3:63"/>
 <a href="numbers.html#K1">REAL</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_5.html#NK2" target="_self">].-infty,</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><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></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="borsuk_5.html#NK4" target="_self">].</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="isomichi.html#E45"><i><font color="Green">Lemma28</font></i></a>, <a class="txt" href="isomichi.html#E1:63"><i><font color="Green">E31</font></i></a></i>;<br/>


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