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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/>





<div><i><font color="Green">E42</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:67_1"/><b>then </b>
<font color="Maroon">c<sub>1</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>1</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="ordinal3.html#D6" target="_self">Def6</a></i>;<br/><a NAME="E3:67_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ordinal2.html#K10">+^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="ordinal3.html#T54" target="_self">Th54</a></i>;<br/><b>hence </b><a NAME="E4:67_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ordinal3.html#K5" target="_self">-^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="ordinal3.html#T65" target="_self">Th65</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_2"/>
not <font color="Maroon">c<sub>3</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:67_2"/><b>then </b>
( <font color="Maroon">c<sub>1</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>  &amp; (  not <font color="Maroon">c<sub>3</sub></font> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) &amp; <font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K11">*^</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <a href="xboole_0.html#K1">{}</a>  <a href="ordinal2.html#K11">*^</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>, <a class="ref" href="ordinal3.html#T38" target="_self">Th38</a>, <a class="ref" href="ordinal2.html#T52">ORDINAL2:52</a>, <a class="ref" href="ordinal2.html#T55">ORDINAL2:55</a></i>;<br/><b>hence </b><a NAME="E3:67_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ordinal3.html#K5" target="_self">-^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="ordinal3.html#D6" target="_self">Def6</a>, <a class="ref" href="ordinal3.html#T69" target="_self">Th69</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:67"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ordinal3.html#K5" target="_self">-^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K5" target="_self">-^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="ordinal3.html#E1:67"><i><font color="Green">E42</font></i></a></i>;<br/>


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