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<a NAME="E1:31_1_1"/>
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">N</font> where <font color="Olive" title="b1">N</font> is   <a href="fintopo7.html#V1" title="FINTOPO7:attr.1">open</a>   <a href="fintopo7.html#M2" title="FINTOPO7:mode.2">a_neighborhood</a> of <font color="Maroon" title="c2">A</font> : verum </span> } </span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">ET</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="31_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">t</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <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"> (  not <font color="Maroon" title="c3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">N</font> where <font color="Olive" title="b1">N</font> is   <a href="fintopo7.html#V1" title="FINTOPO7:attr.1">open</a>   <a href="fintopo7.html#M2" title="FINTOPO7:mode.2">a_neighborhood</a> of <font color="Maroon" title="c2">A</font> : verum </span> } </span>  or <font color="Maroon" title="c3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">ET</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:31_1_1_1"/>
<font color="Maroon" title="c3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">N</font> where <font color="Olive" title="b1">N</font> is   <a href="fintopo7.html#V1" title="FINTOPO7:attr.1">open</a>   <a href="fintopo7.html#M2" title="FINTOPO7:mode.2">a_neighborhood</a> of <font color="Maroon" title="c2">A</font> : verum </span> } </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"> <font color="Maroon" title="c3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">ET</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">N</font> being   <a href="fintopo7.html#V1" title="FINTOPO7:attr.1">open</a>   <a href="fintopo7.html#M2" title="FINTOPO7:mode.2">a_neighborhood</a> of <font color="Maroon" title="c2">A</font><span class="kw"> such that </span><br/><a NAME="E3:31_1_1_1"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
<font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">N</font>
 ;<br/>
<span class="kw">thus </span><a NAME="E4:31_1_1_1"/>
<font color="Maroon" title="c3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">ET</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:31_1_1_1"><span class="lab"><font color="Green" title="E20">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/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:31_1_1"/>
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">N</font> where <font color="Olive" title="b1">N</font> is   <a href="fintopo7.html#V1" title="FINTOPO7:attr.1">open</a>   <a href="fintopo7.html#M2" title="FINTOPO7:mode.2">a_neighborhood</a> of <font color="Maroon" title="c2">A</font> : verum </span> } </span>  is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">ET</font>
 ; <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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