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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="E1:64"/><i><font color="Green">E42</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/>

<a NAME="E2:64"/><i><font color="Green">E43</font></i>: 
( ( <font color="Maroon">c<sub>3</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</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>3</sub></font></span>)</span> ) &amp; ( not <font color="Maroon">c<sub>3</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="ordinal3.html#K5" 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="ordinal3.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E3:64"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="ordinal3.html#T65" target="_self">Th65</a></i>;<br/>
<b>hence </b><a NAME="E4:64"/>
(  not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="ordinal3.html#E1:64"><i><font color="Green">E42</font></i></a>, <a class="txt" href="ordinal3.html#E2:64"><i><font color="Green">E43</font></i></a>, <a class="ref" href="ordinal3.html#T10" target="_self">Th10</a>, <a class="ref" href="ordinal3.html#T66" target="_self">Th66</a></i>;<br/>


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