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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E34">Th32</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: TOPALG_6:32</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">r1</font>, <font color="Olive" title="b3">r2</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b4">t1</font>, <font color="Olive" title="b5">t2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">T</font><br/>  for <font color="Olive" title="b6">p1</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Olive" title="b4">t1</font>,<font color="Olive" title="b5">t2</font>  st <font color="Olive" title="b4">t1</font>,<font color="Olive" title="b5">t2</font> <a href="borsuk_2.html#R1" title="BORSUK_2:pred.1">are_connected</a>  &amp; <font color="Olive" title="b2">r1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">r2</font> holds <br/><font color="Olive" title="b6">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Olive" title="b2">r1</font>,<font color="Olive" title="b3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span> is   <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></div></div>
