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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#V7">natural</a> <a href="ordinal1.html#NM2">Ordinal</a>;<br/>



<b>assume </b><a NAME="E1:29"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>take </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K4" target="_self">lcm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ordinal3.html#K6">div^</a> <font color="Maroon">c<sub>1</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="arytm_3.html#D3" target="_self">ARYTM_3:def 3</a><br/>

<a NAME="E2:29"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K4" target="_self">lcm</a> <font color="Maroon">c<sub>1</sub></font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K4" target="_self">lcm</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="arytm_3.html#D4" target="_self">Def4</a>, <a class="ref" href="arytm_3.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E3:29"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K4" target="_self">lcm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="arytm_3.html#K3" target="_self">*^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ordinal3.html#K6">div^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K4" target="_self">lcm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K4" target="_self">lcm</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="arytm_3.html#K3" target="_self">*^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K4" target="_self">lcm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ordinal3.html#K6">div^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="arytm_3.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E4:29"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="arytm_3.html#K3" target="_self">*^</a> <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#K3" target="_self">*^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K4" target="_self">lcm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ordinal3.html#K6">div^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="arytm_3.html#K3" target="_self">*^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ordinal3.html#K6">div^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K4" target="_self">lcm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="ordinal3.html#T58">ORDINAL3:58</a></i>;<br/>
<b>hence </b><a NAME="E5:29"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ordinal3.html#K6">div^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K4" target="_self">lcm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="arytm_3.html#K3" target="_self">*^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="arytm_3.html#K4" target="_self">lcm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ordinal3.html#K6">div^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="arytm_3.html#E1:29"><i><font color="Green">E22</font></i></a>, <a class="ref" href="ordinal3.html#T36">ORDINAL3:36</a></i>;<br/>


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