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<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_2.html#K2" target="_self">REAL+</a> ;<br/>



<b>assume </b><a NAME="E1:63"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="arytm_3.html#K14">one</a> 
 ;<br/>

<a NAME="E2:63"/><b>then </b><i><font color="Green">E59</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7">RAT+</a>  st <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="arytm_2.html#K3" target="_self">DEDEKIND_CUT</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>2</sub></font> where B is    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7">RAT+</a>  : <font color="Olive">b<sub>2</sub></font> <a href="arytm_3.html#NR4" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> </span>}</span>  )
 
<b>by </b><i><a class="ref" href="arytm_2.html#D3" target="_self">Def3</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="arytm_2.html#K8" target="_self">*'</a> <font color="Maroon">c<sub>5</sub></font> = 
 <a href="arytm_2.html#K4" target="_self">GLUED</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="arytm_2.html#K3" target="_self">DEDEKIND_CUT</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="arytm_2.html#K6" target="_self">*'</a> <span class="p2">(<span class="default"><a href="arytm_2.html#K3" target="_self">DEDEKIND_CUT</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>

<br/>.= 
 <a href="arytm_2.html#K4" target="_self">GLUED</a> <span class="p1">(<span class="default"><a href="arytm_2.html#K3" target="_self">DEDEKIND_CUT</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="arytm_2.html#E1:63"><i><font color="Green">E58</font></i></a>, <a class="txt" href="arytm_2.html#E2:63"><i><font color="Green">E59</font></i></a>, <a class="txt" href="arytm_2.html#E72"><i><font color="Green">Lemma57</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="arytm_2.html#E33"><i><font color="Green">Lemma28</font></i></a></i>
;<br/>


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