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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">x</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_2.html#V1" title="RELAT_2:attr.1">reflexive</a>   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of <font color="Maroon" title="c1">X</font>  st <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</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="Olive" title="b1">R</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">R</font> be   <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a>   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of <font color="Maroon" title="c1">X</font>; <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="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</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> )</span><br/>





<a NAME="E1:9"/>
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c3">R</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="orders_1.html#T12" title="ORDERS_1:th.12">ORDERS_1:12</a></span>;<br/>
<a NAME="E2:9"/><span class="kw">then </span>
<font color="Maroon" title="c3">R</font> <a href="relat_2.html#R1" title="RELAT_2:pred.1">is_reflexive_in</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_2.html#D9" title="RELAT_2:def.9">RELAT_2:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:9"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_2.html#D1" title="RELAT_2:def.1">RELAT_2:def 1</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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