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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>





<b>assume </b><a NAME="E1:76"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<div><i><font color="Green">E34</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:76_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:76_1"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">c<sub>3</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#T55" target="_self">Th55</a></i>;<br/><b>hence </b><a NAME="E3:76_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">c<sub>3</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:76_2"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:76_2_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:76_2_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#R2">c&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="ordinal2.html#E1:76"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/><a NAME="E3:76_2_1"/><b>then </b>
<font color="Maroon">c<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="ordinal1.html#T21">ORDINAL1:21</a></i>;<br/><a NAME="E4:76_2_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="ordinal2.html#E1:76_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="ordinal2.html#T57" target="_self">Th57</a></i>;<br/><b>hence </b><a NAME="E5:76_2_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">c<sub>3</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:76_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">c<sub>3</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:76"/>
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">c<sub>3</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="ordinal2.html#E2:76"><i><font color="Green">E34</font></i></a></i>;<br/>


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