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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#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">R</font> being   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>  st <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> holds <br/><font color="Maroon" title="c2">Y</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Olive" title="b1">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Olive" title="b1">R</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</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">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> implies <font color="Maroon" title="c2">Y</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c3">R</font> )</span><br/>





<a NAME="E1:114"/>
( <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> implies <font color="Maroon" title="c2">Y</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:114"/>
( <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> implies <font color="Maroon" title="c2">Y</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c3">R</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T96" target="_self" title="RELAT_1:th.96">Th127</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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