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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="eqrel_1.html#M1">a_partition</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>;<br/>



<b>thus </b><a NAME="E1:80"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <font color="Maroon">D</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <font color="Maroon">D</font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:80"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <font color="Maroon">D</font></span>)</span>
 ;<br/>

<a NAME="E3:80"/><b>then </b>
 ex <font color="Olive">p</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font> st <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <font color="Maroon">D</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:80"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <font color="Maroon">D</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T6">FUNCT_2:6</a></i>;<br/>


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