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<div><span class="kw">theorem </span><a NAME="T45"><span class="comment"><font color="firebrick">:: FRECHET2:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>  st  not <font color="Olive" title="b1">T</font> is  <a href="pre_topc.html#V7" title="PRE_TOPC:attr.7">T_1</a>  holds <br/> ex <font color="Olive" title="b2">x1</font>, <font color="Olive" title="b3">x2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">T</font> ex <font color="Olive" title="b4">S</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">T</font> st <br/>( <font color="Olive" title="b4">S</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Olive" title="b2">x1</font> &amp; <font color="Olive" title="b2">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">x2</font> &amp; <font color="Olive" title="b4">S</font> <a href="frechet.html#R1" title="FRECHET:pred.1">is_convergent_to</a> <font color="Olive" title="b3">x2</font> ) <span class="kw">by</span> <span class="lab"><a class="txt" href="frechet2.html#E3"><span class="lab"><font color="Green" title="E3">Lm3</font></span></a></span>;<br/></div></div>
