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<span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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></span><br/>





<div><span class="lab"><font color="Green" title="E42">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:65_1"/><span class="lab"><font color="Green" title="E43">A2</font></span>: 
 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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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></span><br/><a NAME="E2:65_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A3</font></span>: 
(  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>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#T35" target="_self" title="ORDINAL3:th.35">Th38</a></span>;<br/><a NAME="E3:65_1"/><span class="lab"><font color="Green" title="E45">A4</font></span>: 
<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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal2.html#T35" title="ORDINAL2:th.35">ORDINAL2:35</a></span>;<br/><a NAME="E4:65_1"/><span class="lab"><font color="Green" title="E46">A5</font></span>: 
<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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal2.html#T38" title="ORDINAL2:th.38">ORDINAL2:38</a></span>;<br/><a NAME="E5:65_1"/>
<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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65_1"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="ordinal3.html#D5" target="_self" title="ORDINAL3:def.5">Def6</a></span>;<br/><span class="kw">hence </span><a NAME="E6:65_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65_1"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="txt" href="#E4:65_1"><span class="lab"><font color="Green" title="E46">A5</font></span></a>, <a class="txt" href="#E3:65_1"><span class="lab"><font color="Green" title="E45">A4</font></span></a>, <a class="ref" href="ordinal3.html#D5" target="_self" title="ORDINAL3:def.5">Def6</a>, <a class="ref" href="ordinal3.html#T56" target="_self" title="ORDINAL3:th.56">Th69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:65_2"/>
<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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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></span><br/><a NAME="E2:65_2"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#D5" target="_self" title="ORDINAL3:def.5">Def6</a></span>;<br/><a NAME="E3:65_2"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#T46" target="_self" title="ORDINAL3:th.46">Th54</a></span>;<br/><span class="kw">hence </span><a NAME="E4:65_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#T52" target="_self" title="ORDINAL3:th.52">Th65</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:65"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E42">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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