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<b>let </b><font color="Maroon" title="c1">T</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/>

<b>assume </b><a NAME="E1:31"/><i><font color="Green" title="E18">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">F</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="compts_1.html#D3" target="_self" title="COMPTS_1:def.3">COMPTS_1:def 3</a><br/>

<b>assume </b><a NAME="E2:31"/><i><font color="Green" title="E19">A2</font></i>: 
( <font color="Maroon" title="c2">F</font> <a href="pre_topc.html#R1" title="PRE_TOPC:pred.1">is_a_cover_of</a> <font color="Maroon" title="c1">T</font> &amp; <font color="Maroon" title="c2">F</font> is <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a> )
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c3">F'</font> = <font color="Maroon" title="c2">F</font> as   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c3">F'</font>
;<br/>

<b>thus </b><a NAME="E4:31"/>
( <font color="Maroon" title="c3">F'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Maroon" title="c3">F'</font> <a href="pre_topc.html#R1" title="PRE_TOPC:pred.1">is_a_cover_of</a> <font color="Maroon" title="c1">T</font> )
 <b>by </b><i><a class="txt" href="compts_1.html#E2:31"><i><font color="Green" title="E19">A2</font></i></a></i>;<br/>

<a NAME="E5:31"/>
(  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; <font color="Maroon" title="c3">F'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> )
 
<b>by </b><i><a class="txt" href="compts_1.html#E1:31"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="finset_1.html#T24" title="FINSET_1:th.24">FINSET_1:24</a></i>;<br/>
<b>hence </b><a NAME="E6:31"/>
<font color="Maroon" title="c3">F'</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="ref" href="finset_1.html#T13" title="FINSET_1:th.13">FINSET_1:13</a></i>;<br/>


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