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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E9">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: TOPALG_7:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a><br/>  for <font color="Olive" title="b3">N</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b1">a</font> <a href="topalg_7.html#K8" title="TOPALG_7:func.8">*</a> <font color="Olive" title="b2">b</font>  ex <font color="Olive" title="b4">N1</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b1">a</font> ex <font color="Olive" title="b5">N2</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b2">b</font> st <br/> for <font color="Olive" title="b6">x</font>, <font color="Olive" title="b7">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  st <font color="Olive" title="b6">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">N1</font> &amp; <font color="Olive" title="b7">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">N2</font> holds <br/><font color="Olive" title="b6">x</font> <a href="topalg_7.html#K8" title="TOPALG_7:func.8">*</a> <font color="Olive" title="b7">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">N</font></div></div>
