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





<div><i><font color="Green" title="E42">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:66_1"/>
<font color="Maroon" title="c3">B</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 ;<br/><a NAME="E2:66_1"/><b>then </b>
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B</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">B</font></span>)</span>
 <b>by </b><i><a class="ref" href="ordinal3.html#D6" target="_self" title="ORDINAL3:def.6">Def6</a></i>;<br/><a NAME="E3:66_1"/><b>then </b>
<font color="Maroon" title="c1">A</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <span class="p1">(<span class="default"><span class="p2">(<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">B</font></span>)</span> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">C</font></span>)</span>
 <b>by </b><i><a class="ref" href="ordinal3.html#T54" target="_self" title="ORDINAL3:th.54">Th54</a></i>;<br/><b>hence </b><a NAME="E4:66_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">B</font></span>)</span> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">C</font>
 <b>by </b><i><a class="ref" href="ordinal3.html#T65" target="_self" title="ORDINAL3:th.65">Th65</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:66_2"/>
not <font color="Maroon" title="c3">B</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 ;<br/><a NAME="E2:66_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">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; (  not <font color="Maroon" title="c3">B</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">C</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">A</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">C</font> or <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) &amp; <font color="Maroon" title="c1">A</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">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>, <a class="ref" href="ordinal3.html#T38" target="_self" title="ORDINAL3:th.38">Th38</a>, <a class="ref" href="ordinal2.html#T52" title="ORDINAL2:th.52">ORDINAL2:52</a>, <a class="ref" href="ordinal2.html#T55" title="ORDINAL2:th.55">ORDINAL2:55</a></i>;<br/><b>hence </b><a NAME="E3:66_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">B</font></span>)</span> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">C</font>
 <b>by </b><i><a class="ref" href="ordinal3.html#D6" target="_self" title="ORDINAL3:def.6">Def6</a>, <a class="ref" href="ordinal3.html#T69" target="_self" title="ORDINAL3:th.69">Th69</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:66"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">B</font></span>)</span> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">C</font>
 <b>by </b><i><a class="txt" href="ordinal3.html#E1:66"><i><font color="Green" title="E42">A1</font></i></a></i>;<br/>


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