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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E32">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: BORSUK_1:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">XX</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><br/>  for <font color="Olive" title="b2">X</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Olive" title="b1">XX</font><br/>  for <font color="Olive" title="b3">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">X</font><br/>  for <font color="Olive" title="b4">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">XX</font>  holds <br/>(  not <font color="Olive" title="b4">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="borsuk_1.html#K13" title="BORSUK_1:func.13">TrivExt</a> <font color="Olive" title="b3">D</font> or <font color="Olive" title="b4">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">D</font> or  ex <font color="Olive" title="b5">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">XX</font> st <br/>(  not <font color="Olive" title="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b2">X</font> &amp; <font color="Olive" title="b4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b5">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> ) )</div></div>
