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<b>let </b><font color="Maroon" title="c1">T</font> be  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/><b>let </b><font color="Maroon" title="c2">A</font> be  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="Maroon" title="c1">T</font>;<br/><b>let </b><font color="Maroon" title="c3">y</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K13" title="BORSUK_1:func.13">space</a> <font color="Maroon" title="c2">A</font></span>)</span>;<br/>





<b>reconsider </b><font color="Maroon" title="c4">y</font> = <font color="Maroon" title="c3">y</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">A</font> <b>by </b><i><a class="ref" href="borsuk_1.html#D10" title="BORSUK_1:def.10">BORSUK_1:def 10</a></i>;<br/>
<span class="p1">(<span class="default"><a href="borsuk_1.html#K14" title="BORSUK_1:func.14">Proj</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Maroon" title="c4">y</font> = 
<span class="p1">(<span class="default"><a href="borsuk_1.html#K1" title="BORSUK_1:func.1">proj</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Maroon" title="c4">y</font>
<b>by </b><i><a class="ref" href="borsuk_1.html#D11" title="BORSUK_1:def.11">BORSUK_1:def 11</a></i>
<br/>.= 
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c4">y</font>
<b>by </b><i><a class="ref" href="borsuk_1.html#T31" title="BORSUK_1:th.31">BORSUK_1:31</a></i>
;<br/>
<b>hence </b><a NAME="E3:1"/>
<span class="p1">(<span class="default"><a href="borsuk_1.html#K14" title="BORSUK_1:func.14">Proj</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c3">y</font>
 ;<br/>


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