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<span class="kw">set </span><font color="Maroon" title="c3">S</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">ET</font>;<br/>
<a NAME="E1:16_1_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">ET</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">ET</font>
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">S</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">ET</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">ET</font> ;<br/>
<a NAME="E3:16_1_1"/>
 for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ET</font>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">A</font> holds <br/><font color="Maroon" title="c4">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="fintopo2.html#K6" title="FINTOPO2:func.6">U_FMT</a> <font color="Olive" title="b1">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo7.html#T10" target="_self" onmouseover="rs('fintopo7/T10')" onmouseout="rh()">Th6</a></span>;<br/>
<a NAME="E4:16_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<font color="Maroon" title="c4">S</font> is    <a href="fintopo7.html#M2" title="FINTOPO7:mode.2">a_neighborhood</a> of <font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo7.html#D6" target="_self" onmouseover="rs('fintopo7/D6')" onmouseout="rh()">Def6</a></span>;<br/>
<a NAME="E5:16_1_1"/>
<font color="Maroon" title="c4">S</font> is  <a href="fintopo7.html#V1" title="FINTOPO7:attr.1">open</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo7.html#T10" target="_self" onmouseover="rs('fintopo7/T10')" onmouseout="rh()">Th6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:16_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being    <a href="fintopo7.html#M2" title="FINTOPO7:mode.2">a_neighborhood</a> of <font color="Maroon" title="c2">A</font> st <font color="Olive">b<sub>1</sub></font> is  <a href="fintopo7.html#V1" title="FINTOPO7:attr.1">open</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:16_1_1"><span class="lab"><font color="Green" title="E13">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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