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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E17">Th15</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: FUNCTOR0:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">B</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">B</font><br/>  for <font color="Olive" title="b4">f</font> being   <a href="functor0.html#NM1" title="FUNCTOR0:NM.1">bifunction</a> of <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>  st <font color="Olive" title="b4">f</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b1">A</font>,<font color="Olive" title="b1">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b3">b</font>,<font color="Olive" title="b3">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/>( <font color="Olive" title="b4">f</font> is  <a href="functor0.html#V1" title="FUNCTOR0:attr.1">Covariant</a>  &amp; <font color="Olive" title="b4">f</font> is  <a href="functor0.html#V2" title="FUNCTOR0:attr.2">Contravariant</a>  )</div></div>
