<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">:]</a></span> holds   <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K8" title="BORSUK_1:func.8">Base-Appr</a> <font color="Olive" title="b1">A</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">:]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K8" title="BORSUK_1:func.8">Base-Appr</a> <font color="Maroon" title="c3">A</font></span>)</span></span><br/>



<a NAME="E1:66"/>
(  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K8" title="BORSUK_1:func.8">Base-Appr</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> &amp;  <a href="borsuk_1.html#K8" title="BORSUK_1:func.8">Base-Appr</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="borsuk_1.html#K8" title="BORSUK_1:func.8">Base-Appr</a> <font color="Maroon" title="c3">A</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T52" target="_self" title="BORSUK_1:th.52">Th52</a>, <a class="ref" href="borsuk_1.html#T54" target="_self" title="BORSUK_1:th.54">Th54</a>, <a class="ref" href="tops_1.html#T44" title="TOPS_1:th.44">TOPS_1:44</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:66"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K8" title="BORSUK_1:func.8">Base-Appr</a> <font color="Maroon" title="c3">A</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T95" title="ZFMISC_1:th.95">ZFMISC_1:95</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K8" title="BORSUK_1:func.8">Base-Appr</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">A</font></span><br/>

<a NAME="E3:66"/>
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K8" title="BORSUK_1:func.8">Base-Appr</a> <font color="Maroon" title="c3">A</font></span>)</span> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T51" target="_self" title="BORSUK_1:th.51">Th51</a>, <a class="ref" href="tops_2.html#T26" title="TOPS_2:th.26">TOPS_2:26</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:66"/>
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K8" title="BORSUK_1:func.8">Base-Appr</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T53" target="_self" title="BORSUK_1:th.53">Th53</a>, <a class="ref" href="tops_1.html#T56" title="TOPS_1:th.56">TOPS_1:56</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
