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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="E1:62"/><i><font color="Green">E42</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/>

<a NAME="E2:62"/><b>then </b><i><font color="Green">E43</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> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="ordinal3.html#D6" target="_self">Def6</a></i>;<br/>
<div><i><font color="Green">E44</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:62_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:62_1"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="ordinal2.html#K10">+^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="ordinal3.html#E1:62"><i><font color="Green">E42</font></i></a>, <a class="ref" href="ordinal3.html#D6" target="_self">Def6</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E3:62_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="ordinal2.html#K10">+^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K10">+^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="ordinal3.html#D6" target="_self">Def6</a></i>;<br/><a NAME="E4:62_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K10">+^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ordinal2.html#K10">+^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K10">+^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ordinal3.html#E2:62"><i><font color="Green">E43</font></i></a>, <a class="ref" href="ordinal3.html#T33" target="_self">Th33</a></i>;<br/><a NAME="E5:62_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ordinal2.html#K10">+^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="ordinal3.html#T24" target="_self">Th24</a></i>;<br/><b>hence </b><a NAME="E6:62_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>2</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ordinal3.html#K5" target="_self">-^</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="hs2(this)" href="javascript:()" title="62_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:62_2"/>
not <font color="Maroon">c<sub>2</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:62_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="ordinal3.html#K5" target="_self">-^</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#D6" target="_self">Def6</a></i>;<br/><b>hence </b><a NAME="E3:62_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>2</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ordinal3.html#K5" target="_self">-^</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>
<b>hence </b><a NAME="E5:62"/>
<font color="Maroon">c<sub>3</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>2</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="ordinal3.html#E3:62"><i><font color="Green">E44</font></i></a></i>;<br/>


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