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<span class="kw">let </span><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#NM3" title="ORDINAL1:NM.3">Ordinal</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">A</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c2">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">C</font> implies <font color="Maroon" title="c2">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">C</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c1">A</font> )</span><br/>





<a NAME="E1:62"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#T52" target="_self" onmouseover="rs('ordinal3/T52')" onmouseout="rh()">Th52</a></span>;<br/>
<a NAME="E2:62"/>
<font color="Maroon" title="c1">A</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">A</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c2">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#T24" target="_self" onmouseover="rs('ordinal3/T24')" onmouseout="rh()">Th24</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:62"/>
( <font color="Maroon" title="c1">A</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c2">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">C</font> implies <font color="Maroon" title="c2">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">C</font> <a href="ordinal3.html#K5" title="ORDINAL3:func.5">-^</a> <font color="Maroon" title="c1">A</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="ref" href="ordinal3.html#T53" target="_self" onmouseover="rs('ordinal3/T53')" onmouseout="rh()">Th53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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