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<span class="kw">set </span><font color="Maroon" title="c4">x</font> =  the    <a href="petri.html#M1" title="PETRI:mode.1">Element</a> of <font color="Maroon" title="c3">r</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">y</font>, <font color="Maroon" title="c6">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E2:33_1_1"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
 the    <a href="petri.html#M1" title="PETRI:mode.1">Element</a> of <font color="Maroon" title="c3">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c6">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D1" onmouseover="rs('relat_1/D1')" onmouseout="rh()">RELAT_1:def 1</a></span>;<br/>
<a NAME="E3:33_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">r</font> <a href="relset_1.html#K3" title="RELSET_1:func.3">~</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33_1_1"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="relat_1.html#D7" onmouseover="rs('relat_1/D7')" onmouseout="rh()">RELAT_1:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:33_1_1"/>
<font color="Maroon" title="c3">r</font> <a href="relat_1.html#K2" title="RELAT_1:func.2">~</a>  is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>
 ; <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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