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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E33">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: TOPALG_6:31</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#L1" title="PRE_TOPC:struct.1">TopStruct</a> <br/>  for <font color="Olive" title="b2">c</font> being   <a href="topalg_6.html#V7" title="TOPALG_6:attr.7">with_endpoints</a>  <a href="topalg_6.html#NM1" title="TOPALG_6:NM.1">Curve</a> of <font color="Olive" title="b1">T</font> holds <br/> (  <a href="topalg_6.html#K2" title="TOPALG_6:func.2">the_first_point_of</a> <font color="Olive" title="b2">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">c</font> &amp;  <a href="topalg_6.html#K3" title="TOPALG_6:func.3">the_last_point_of</a> <font color="Olive" title="b2">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">c</font> )</div></div>
