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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>

<a NAME="E1:74"/>
(  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <a href="xboole_0.html#K1">{}</a>  <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>1</sub></font> &amp; ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <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>  ) )
 
<b>by </b><i><a class="ref" href="ordinal2.html#T52">ORDINAL2:52</a></i>;<br/>
<b>hence </b><a NAME="E2:74"/>
<a href="xboole_0.html#K1">{}</a>  <a href="ordinal3.html#K6" target="_self">div^</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="ordinal3.html#D7" target="_self">Def7</a>, <a class="ref" href="ordinal3.html#T81" target="_self">Th81</a></i>;<br/>

<b>thus </b><a href="xboole_0.html#K1">{}</a>  <a href="ordinal3.html#K7" target="_self">mod^</a> <font color="Maroon">c<sub>1</sub></font> = 
<a href="xboole_0.html#K1">{}</a>  <a href="ordinal3.html#K5" target="_self">-^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xboole_0.html#K1">{}</a>  <a href="ordinal3.html#K6" target="_self">div^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="ordinal3.html#T69" target="_self">Th69</a></i>
;<br/>

<b>thus </b><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K7" target="_self">mod^</a> <a href="xboole_0.html#K1">{}</a>  = 
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K6" target="_self">div^</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="ordinal2.html#K11">*^</a> <a href="xboole_0.html#K1">{}</a> </span>)</span>

<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="ordinal2.html#T55">ORDINAL2:55</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="ordinal3.html#T69" target="_self">Th69</a></i>
;<br/>


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