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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/>





<b>assume </b><a NAME="E1:63"/><i><font color="Green" title="E42">A1</font></i>: 
<font color="Maroon" title="c1">A</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">B</font>
 ;<br/>

<div><i><font color="Green" title="E43">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_1"/>
<font color="Maroon" title="c3">C</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 ;<br/><a NAME="E2:63_1"/><b>then </b>
( <font color="Maroon" title="c3">C</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c3">C</font></span>)</span> )
 <b>by </b><i><a class="txt" href="ordinal3.html#E1:63"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="ordinal3.html#D6" target="_self" title="ORDINAL3:def.6">Def6</a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E3:63_1"/><b>then </b>
<font color="Maroon" title="c3">C</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c3">C</font></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">C</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c3">C</font></span>)</span>
 <b>by </b><i><a class="txt" href="ordinal3.html#E1:63"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="ordinal3.html#D6" target="_self" title="ORDINAL3:def.6">Def6</a></i>;<br/><b>hence </b><a NAME="E4:63_1"/>
<font color="Maroon" title="c1">A</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c3">C</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">B</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c3">C</font>
 <b>by </b><i><a class="ref" href="ordinal3.html#T26" target="_self" title="ORDINAL3:th.26">Th26</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_2"/>
not <font color="Maroon" title="c3">C</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 ;<br/><a NAME="E2:63_2"/><b>then </b>
<font color="Maroon" title="c1">A</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="ordinal3.html#D6" target="_self" title="ORDINAL3:def.6">Def6</a></i>;<br/><b>hence </b><a NAME="E3:63_2"/>
<font color="Maroon" title="c1">A</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c3">C</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">B</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c3">C</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:63"/>
<font color="Maroon" title="c1">A</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c3">C</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">B</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c3">C</font>
 <b>by </b><i><a class="txt" href="ordinal3.html#E2:63"><i><font color="Green" title="E43">A2</font></i></a></i>;<br/>


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