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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7">RAT+</a> ;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</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><b>that </b><br/><a NAME="E1:20"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:20"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:20_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="arytm_2.html#R1" target="_self">&lt;='</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:20_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</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>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="arytm_3.html#R3">&lt;='</a> <font color="Olive">b<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="arytm_2.html#E1:20"><i><font color="Green">E20</font></i></a>, <a class="txt" href="arytm_2.html#E2:20"><i><font color="Green">E21</font></i></a>, <a class="ref" href="arytm_2.html#D5" target="_self">Def5</a></i>;<br/><b>hence </b><a NAME="E3:20_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="arytm_3.html#R3">&lt;='</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="arytm_2.html#E1:20"><i><font color="Green">E20</font></i></a>, <a class="txt" href="arytm_2.html#E2:20"><i><font color="Green">E21</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E4:20"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="arytm_3.html#R3">&lt;='</a> <font color="Maroon">c<sub>4</sub></font> implies <font color="Maroon">c<sub>5</sub></font> <a href="arytm_2.html#R1" target="_self">&lt;='</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="arytm_2.html#E1:20"><i><font color="Green">E20</font></i></a>, <a class="txt" href="arytm_2.html#E2:20"><i><font color="Green">E21</font></i></a>, <a class="ref" href="arytm_2.html#D5" target="_self">Def5</a></i>;<br/>


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