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<b>let </b><font color="Maroon">F</font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">T</font>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:43_1_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">F</font> is    <a href="yellow13.html#M1" target="_self">basis</a> of <font color="Maroon">p</font>
 ;<br/><b>let </b><font color="Maroon">A</font> be    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">p</font>;<br/><a NAME="E2:43_1_1_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="connsp_2.html#D1">CONNSP_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">P</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E4:43_1_1_1"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">P</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">P</font> &amp; <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> )
 <b>by </b><i>, </i>;<br/><b>reconsider </b><font color="Maroon">P</font> = <font color="Maroon">P</font> as    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">p</font> <b>by </b><i>, <a class="ref" href="connsp_2.html#D1">CONNSP_2:def 1</a></i>;<br/><b>take </b><font color="Maroon">P</font> = <font color="Maroon">P</font>;<br/><b>thus </b><a NAME="E6:43_1_1_1"/>
( <font color="Maroon">P</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> )
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:43_1_1"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">A</font> being   <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">p</font>  ex <font color="Olive">P</font> being   <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">p</font> st <br/>( <font color="Olive">P</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Olive">P</font> <a href="tarski.html#R1">c=</a> <font color="Olive">A</font> )
 ;<br/>

<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow13.html#D1" target="_self">YELLOW13:def 1</a><br/>

<b>assume </b><a NAME="E3:43_1_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E4:43_1_1"/><b>then </b>
<font color="Maroon">A</font> is    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="connsp_2.html#D1">CONNSP_2:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">P</font> being    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">p</font><b> such that </b><br/><a NAME="E6:43_1_1"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">P</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> )
 <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">P</font>
;<br/>

<b>thus </b><a NAME="E7:43_1_1"/>
( <font color="Maroon">P</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">P</font> &amp; <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> )
 <b>by </b><i>, <a class="ref" href="connsp_2.html#D1">CONNSP_2:def 1</a></i>;<br/>


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