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<div><span class="kw">theorem </span><a NAME="T13"><span class="comment"><font color="firebrick">:: FRIENDS1:13</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">FSG</font> being   <a href="friends1.html#NM1" title="FRIENDS1:NM.1">Friendship_Graph</a><br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <font color="Olive" title="b1">FSG</font>  st <font color="Olive" title="b2">x</font> is  <a href="friends1.html#V1" title="FRIENDS1:attr.1">universal_friend</a>  &amp; <font color="Olive" title="b2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">y</font> holds <br/> ex <font color="Olive" title="b4">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>(  <a href="relat_1.html#K9" title="RELAT_1:func.9">Im</a> (<font color="Olive" title="b1">FSG</font>,<font color="Olive" title="b3">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b2">x</font>,<font color="Olive" title="b4">z</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  <a href="relat_1.html#K9" title="RELAT_1:func.9">Im</a> (<font color="Olive" title="b1">FSG</font>,<font color="Olive" title="b4">z</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )</div></div>
