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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="ordinal1.html#V3">ordinal</a>  <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7">RAT+</a> ;<br/>

<b>assume </b><a NAME="E1:14"/>
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being  <a href="ordinal1.html#V3">ordinal</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E3:14"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="ordinal3.html#T30">ORDINAL3:30</a></i>;<br/>
<a NAME="E4:14"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K5">omega</a> 
 
<b>by </b><i><a class="txt" href="numbers.html#E3:14"><i><font color="Green">E11</font></i></a>, <a class="ref" href="arytm_3.html#T1">ARYTM_3:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7">RAT+</a>  <b>by </b><i><a class="ref" href="arytm_3.html#T34">ARYTM_3:34</a></i>;<br/>
<a NAME="E6:14"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="arytm_3.html#K11">+</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="numbers.html#E3:14"><i><font color="Green">E11</font></i></a>, <a class="ref" href="arytm_3.html#T64">ARYTM_3:64</a></i>;<br/>
<b>hence </b><a NAME="E7:14"/>
<font color="Maroon">c<sub>1</sub></font> <a href="arytm_3.html#R3">&lt;='</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="arytm_3.html#D13">ARYTM_3:def 13</a></i>;<br/>


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