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<div><span class="kw">theorem </span><a NAME="T1"><span class="comment"><font color="firebrick">:: BROUWER:1</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">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><br/>  for <font color="Olive" title="b3">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="brouwer.html#K1" title="BROUWER:func.1">DiffElems</a> (<font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">T</font>) iff  ex <font color="Olive" title="b4">s</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">S</font> ex <font color="Olive" title="b5">t</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b2">T</font> st <br/>( <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[</a><span class="default"><font color="Olive" title="b4">s</font>,<font color="Olive" title="b5">t</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">]</a></span> &amp; <font color="Olive" title="b4">s</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">t</font> ) ) ;<br/></div></div>
