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<span class="kw">let </span><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">A</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"> ( <font color="Maroon" title="c1">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c1">C</font> implies <font color="Maroon" title="c2">A</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c3">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:62"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
<font color="Maroon" title="c1">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c1">C</font> or <font color="Maroon" title="c2">A</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c3">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C</font> )</span><br/>

<a NAME="E2:62"/><span class="lab"><font color="Green" title="E43">A2</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c1">C</font></span>)</span> <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> <font color="Maroon" title="c1">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>;<br/>
<a NAME="E3:62"/>
(  not <font color="Maroon" title="c3">B</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">A</font> implies <font color="Maroon" title="c2">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="ref" href="ordinal3.html#D5" target="_self" title="ORDINAL3:def.5">Def6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:62"/>
(  not <font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c1">C</font> or <font color="Maroon" title="c2">A</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c3">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E2:62"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="ordinal3.html#T8" target="_self" title="ORDINAL3:th.8">Th10</a>, <a class="ref" href="ordinal3.html#T53" target="_self" title="ORDINAL3:th.53">Th66</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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