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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#NM2">Ordinal</a>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="68_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:68_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="68_1_1_1"><b>suppose </b></a><a NAME="E1:68_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><a NAME="E2:68_1_1_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <br/>( <font color="Maroon">c<sub>1</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>1</sub></font> <a href="ordinal3.html#K6" target="_self">div^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ordinal2.html#K10">+^</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="ordinal3.html#D7" target="_self">Def7</a></i>;<br/><b>hence </b><a NAME="E3:68_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K6" target="_self">div^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="ordinal3.html#T27" target="_self">Th27</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="68_1_1_2"><b>suppose </b></a><a NAME="E1:68_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><a NAME="E2:68_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K6" target="_self">div^</a> <font color="Maroon">c<sub>2</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></i>;<br/><a NAME="E3:68_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K6" target="_self">div^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</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="E4:68_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K6" target="_self">div^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:68"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K6" target="_self">div^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


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