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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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"> <span class="p1">(<span class="default"><a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c2">Y</font></span>)</span></span><br/>



<a NAME="E1:74"/>
( <span class="p1">(<span class="default"><a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <font color="Maroon" title="c2">Y</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">Y</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <font color="Maroon" title="c1">X</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xtuple_0.html#T37" target="_self" onmouseover="rs('xtuple_0/T37')" onmouseout="rh()">Th37</a></span>;<br/>
<a NAME="E2:74"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">Y</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T13" onmouseover="rs('xboole_1/T13')" onmouseout="rh()">XBOOLE_1:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:74"/>
<span class="p1">(<span class="default"><a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="xtuple_0.html#K12" title="XTUPLE_0:func.12">proj2_3</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xtuple_0.html#T35" target="_self" onmouseover="rs('xtuple_0/T35')" onmouseout="rh()">Th35</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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