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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: FUZZY_4:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</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">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b4">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">Y</font> holds <br/> ( ( <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">y</font> implies <span class="p1">(<span class="default"><a href="fuzzy_4.html#K4" title="FUZZY_4:func.4">Imf</a> (<font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Olive" title="b3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">y</font> implies <span class="p1">(<span class="default"><a href="fuzzy_4.html#K4" title="FUZZY_4:func.4">Imf</a> (<font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) )</div></div>
