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<a NAME="E1:12_1_1"/>
 <a href="toprealb.html#K2" title="TOPREALB:func.2">IntIntervals</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> is <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topalg_2.html#K2" title="TOPALG_2:func.2">R^1</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_2.html#D1" title="TOPS_2:def.1">TOPS_2:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c10">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="toprealb.html#K2" title="TOPREALB:func.2">IntIntervals</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> or <font color="Maroon" title="c10">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> )</span><br/>

<b>assume </b><a NAME="E1:12_1_1_1"/>
<font color="Maroon" title="c10">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="toprealb.html#K2" title="TOPREALB:func.2">IntIntervals</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a></span><br/>

<a NAME="E2:12_1_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  st <font color="Maroon" title="c10">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">n</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">b</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">n</font></span>)</span></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 
;<br/>
<b>hence </b><a NAME="E3:12_1_1_1"/>
<font color="Maroon" title="c10">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="ref" href="jordan6.html#T46" title="JORDAN6:th.46">JORDAN6:46</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:12_1_1"/>
 <a href="toprealb.html#K1" title="TOPREALB:func.1">IntIntervals</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> is  <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a> <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <a href="topalg_2.html#K2" title="TOPALG_2:func.2">R^1</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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