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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E46">Th58</font></span>: <a NAME="T58"><span class="comment"><font color="firebrick">:: TOPGEN_5:58</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b2">w</font> being   <a href="rat_1.html#NM1" title="RAT_1:NM.1">Rational</a>  ex <font color="Olive" title="b3">f</font> being   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="topgen_3.html#K2" title="TOPGEN_3:func.2">Sorgenfrey-line</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> st <br/> for <font color="Olive" title="b4">a</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topgen_3.html#K2" title="TOPGEN_3:func.2">Sorgenfrey-line</a> holds <br/> ( ( <font color="Olive" title="b4">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">w</font></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span> implies <font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) &amp; (  not <font color="Olive" title="b4">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">w</font></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span> implies <font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) )</div></div>
