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<span class="kw">reconsider </span><font color="Maroon" title="c2">F</font> =  <a href="fintopo7.html#K4" title="FINTOPO7:func.4">Family_open_set</a> <font color="Maroon" title="c1">ET</font> as   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">ET</font> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c3">x</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="ref" href="fintopo7.html#D13" target="_self" onmouseover="rs('fintopo7/D13')" onmouseout="rh()">FINTOPO7:def 13</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">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fintopo7.html#K4" title="FINTOPO7:func.4">Family_open_set</a> <font color="Maroon" title="c1">ET</font> or <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <span class="p1">(<span class="default"><a href="fintopo7.html#K4" title="FINTOPO7:func.4">Family_open_set</a> <font color="Maroon" title="c1">ET</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E2:36_1_1"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fintopo7.html#K4" title="FINTOPO7:func.4">Family_open_set</a> <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"> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <span class="p1">(<span class="default"><a href="fintopo7.html#K4" title="FINTOPO7:func.4">Family_open_set</a> <font color="Maroon" title="c1">ET</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">B</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">ET</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#T41" onmouseover="rs('subset_1/T41')" onmouseout="rh()">SUBSET_1:41</a></span>;<br/>
<a NAME="E4:36_1_1"/><span class="lab"><font color="Green" title="E24">A2</font></span>: 
<font color="Maroon" title="c4">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="fintopo7.html#K4" title="FINTOPO7:func.4">Family_open_set</a> <font color="Maroon" title="c1">ET</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1_1"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#T31" onmouseover="rs('zfmisc_1/T31')" onmouseout="rh()">ZFMISC_1:31</a></span>;<br/>
<a NAME="E5:36_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c4">B</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E6:36_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <span class="p1">(<span class="default"><a href="fintopo7.html#K4" title="FINTOPO7:func.4">Family_open_set</a> <font color="Maroon" title="c1">ET</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1_1"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="ref" href="cantor_1.html#D1" onmouseover="rs('cantor_1/D1')" onmouseout="rh()">CANTOR_1:def 1</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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