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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">Y</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">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="borsuk_1.html#K5" target="_self">:]</a></span>;<br/><b>let </b><font color="Maroon">H</font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="borsuk_1.html#K5" target="_self">:]</a></span>;<br/>







<a NAME="E1:61"/><i><font color="Green">E24</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="borsuk_1.html#K5" target="_self">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i/>;<br/>
<b>assume </b><a NAME="E2:61"/>
for <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H</font> holds <br/>( <font color="Olive">e</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> &amp;  ex <font color="Olive">X1</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> ex <font color="Olive">Y1</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font> st <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K6" target="_self">[:</a><span class="default"><font color="Olive">X1</font>,<font color="Olive">Y1</font></span><a href="borsuk_1.html#K6" target="_self">:]</a></span> )
 ;<br/>

<b>hence </b><a NAME="E3:61"/>
<span class="p1"><a href="borsuk_1.html#K6" target="_self">[:</a><span class="default"><span class="p2">(<span class="default"><a href="setfam_1.html#K5">union</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="borsuk_1.html#K11" target="_self">Pr1</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">H</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="setfam_1.html#K6">meet</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="borsuk_1.html#K12" target="_self">Pr2</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">H</font></span>)</span></span>)</span></span><a href="borsuk_1.html#K6" target="_self">:]</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <b>by </b><i>, </i>;<br/>


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