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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <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>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="arytm_2.html#K8" target="_self">*'</a> <span class="p1">(<span class="default"><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></span>)</span> = 
<font color="Maroon">c<sub>3</sub></font> <a href="arytm_2.html#K8" target="_self">*'</a> <span class="p1">(<span class="default"><a href="arytm_2.html#K4" target="_self">GLUED</a> <span class="p2">(<span class="default"><span class="p3">(<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="p3">(<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></span>)</span>

<br/>.= 
 <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>3</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> <span class="p3">(<span class="default"><a href="arytm_2.html#K4" target="_self">GLUED</a> <span class="p4">(<span class="default"><span class="p5">(<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="p5">(<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></span>)</span></span>)</span></span>)</span>

<br/>.= 
 <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>3</sub></font></span>)</span> <a href="arytm_2.html#K6" target="_self">*'</a> <span class="p2">(<span class="default"><span class="p3">(<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="p3">(<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></span>)</span>
<b>by </b><i><a class="txt" href="arytm_2.html#E21"><i><font color="Green">Lemma16</font></i></a></i>
<br/>.= 
 <a href="arytm_2.html#K4" target="_self">GLUED</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_2.html#K3" target="_self">DEDEKIND_CUT</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="arytm_2.html#K6" target="_self">*'</a> <span class="p3">(<span class="default"><a href="arytm_2.html#K3" target="_self">DEDEKIND_CUT</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></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>
<b>by </b><i><a class="txt" href="arytm_2.html#E62"><i><font color="Green">Lemma52</font></i></a></i>
<br/>.= 
 <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> <span class="p3">(<span class="default"><a href="arytm_2.html#K4" target="_self">GLUED</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="arytm_2.html#K3" target="_self">DEDEKIND_CUT</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="arytm_2.html#K6" target="_self">*'</a> <span class="p5">(<span class="default"><a href="arytm_2.html#K3" target="_self">DEDEKIND_CUT</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></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>
<b>by </b><i><a class="txt" href="arytm_2.html#E21"><i><font color="Green">Lemma16</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="arytm_2.html#K4" target="_self">GLUED</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_2.html#K3" target="_self">DEDEKIND_CUT</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="arytm_2.html#K6" target="_self">*'</a> <span class="p3">(<span class="default"><a href="arytm_2.html#K3" target="_self">DEDEKIND_CUT</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="arytm_2.html#K8" target="_self">*'</a> <font color="Maroon">c<sub>5</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="arytm_2.html#K8" target="_self">*'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="arytm_2.html#K8" target="_self">*'</a> <font color="Maroon">c<sub>5</sub></font>

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