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<b>let </b><font color="Maroon" title="c4">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_2.html#K2" title="ARYTM_2:func.2">REAL+</a> ;<br/>

<b>assume </b><a NAME="E1:61"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a> 
 ;<br/>

<a NAME="E2:61"/><b>then </b>
 <a href="arytm_2.html#K3" title="ARYTM_2:func.3">DEDEKIND_CUT</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a> 
 
<b>by </b><i><a class="txt" href="arytm_2.html#E20"><i><font color="Green" title="E15">Lm11</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">B</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="arytm_2.html#K1" title="ARYTM_2:func.1">DEDEKIND_CUTS</a> <b> such that </b><br/><a NAME="E4:61"/><i><font color="Green" title="E58">A1</font></i>: 
<span class="p1">(<span class="default"><a href="arytm_2.html#K3" title="ARYTM_2:func.3">DEDEKIND_CUT</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="arytm_2.html#K6" title="ARYTM_2:func.6">*'</a> <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_2.html#K3" title="ARYTM_2:func.3">DEDEKIND_CUT</a> <font color="Maroon" title="c3">rone</font>
 <b>by </b><i><a class="txt" href="arytm_2.html#E71"><i><font color="Green" title="E57">Lm44</font></i></a></i>;<br/>
<b>take </b><font color="Maroon" title="c6">y</font> =  <a href="arytm_2.html#K4" title="ARYTM_2:func.4">GLUED</a> <font color="Maroon" title="c5">B</font>;<br/>

<b>thus </b><font color="Maroon" title="c4">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c6">y</font> = 
 <a href="arytm_2.html#K4" title="ARYTM_2:func.4">GLUED</a> <span class="p1">(<span class="default"><a href="arytm_2.html#K3" title="ARYTM_2:func.3">DEDEKIND_CUT</a> <font color="Maroon" title="c3">rone</font></span>)</span>
<b>by </b><i><a class="txt" href="arytm_2.html#E4:61"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="arytm_2.html#E22"><i><font color="Green" title="E17">Lm13</font></i></a></i>
<br/>.= 
 <a href="arytm_3.html#K14" title="ARYTM_3:func.14">one</a> 
<b>by </b><i><a class="txt" href="arytm_2.html#E34"><i><font color="Green" title="E29">Lm24</font></i></a></i>
;<br/>


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