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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E33">Th32</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: TOPGEN_3:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="topgen_3.html#K3" title="TOPGEN_3:func.3">continuum</a>  holds <br/> ex <font color="Olive" title="b2">x</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> ex <font color="Olive" title="b3">q</font> being   <a href="rat_1.html#NM1" title="RAT_1:NM.1">Rational</a> st <br/>( <font color="Olive" title="b2">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">q</font> &amp;  not <span class="p1"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">q</font></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <font color="Olive" title="b1">X</font> )</div></div>
