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<b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="borsuk_1.html#K20">I[01]</a> ;<br/>

<b>assume </b><a NAME="E1:39"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_1.html#K20">I[01]</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<a NAME="E2:39"/><i><font color="Green">E47</font></i>: 
0 <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T48">RCOMP_1:48</a></i>;<br/>
<a NAME="E3:39"/><i><font color="Green">E49</font></i>: 
1 <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T48">RCOMP_1:48</a></i>;<br/>
<b>reconsider </b><font color="Maroon">Q0</font> = <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">0</span><a href="seq_4.html#K1">}</a></span> as   <a href="struct_0.html#NM2">Subset</a> of <a href="borsuk_1.html#K20">I[01]</a>  <b>by </b><i>, <a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E5:39"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">Q0</font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i>, <a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a>, <a class="ref" href="pcomps_1.html#T10">PCOMPS_1:10</a></i>;<br/>
<b>reconsider </b><font color="Maroon">Q1</font> = <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span> as   <a href="struct_0.html#NM2">Subset</a> of <a href="borsuk_1.html#K20">I[01]</a>  <b>by </b><i>, <a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E7:39"/>
<font color="Maroon">Q1</font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i>, <a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a>, <a class="ref" href="pcomps_1.html#T10">PCOMPS_1:10</a></i>;<br/>
<a NAME="E8:39"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">Q0</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q1</font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i>, <a class="ref" href="tops_1.html#T36">TOPS_1:36</a></i>;<br/>
<a NAME="E9:39"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">Q0</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>;<br/>
<a NAME="E10:39"/>
<span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <a href="borsuk_1.html#K20">I[01]</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">Q0</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q1</font></span>)</span> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i>, <a class="ref" href="pre_topc.html#D6">PRE_TOPC:def 6</a></i>;<br/>
<b>hence </b><a NAME="E11:39"/>
<font color="Maroon">P</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i>, </i>;<br/>


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