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<b>let </b><font color="Maroon" title="c1">T</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">T</font> is <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a> iff  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> )</span><br/>

<b>thus </b><a NAME="E1:6"/>
( <font color="Maroon" title="c1">T</font> is <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a> implies  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> implies <font color="Maroon" title="c1">T</font> is <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:6_1"/><i><font color="Green" title="E4">A1</font></i>: 
<font color="Maroon" title="c1">T</font> is <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a></span><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#D7" target="_self" title="COMPTS_1:def.7">COMPTS_1:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">F</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</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> implies  ex <font color="Olive" title="b1">G</font> being  <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Olive" title="b1">G</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font> &amp; <font color="Olive" title="b1">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> ) )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E2:6_1"/><i><font color="Green" title="E5">A2</font></i>: 
<font color="Maroon" title="c2">F</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font>
 <b>and </b><br/><a NAME="E3:6_1"/><i><font color="Green" title="E6">A3</font></i>: 
<font color="Maroon" title="c2">F</font> is <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">G</font> being  <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Olive" title="b1">G</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font> &amp; <font color="Olive" title="b1">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> )</span><br/>

<a NAME="E4:6_1"/>
<font color="Maroon" title="c2">F</font> is   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">Cover</a> of <font color="Maroon" title="c1">T</font>
 
<b>by </b><i><a class="txt" href="#E2:6_1"><i><font color="Green" title="E5">A2</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">G</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E6:6_1"/><i><font color="Green" title="E7">A4</font></i>: 
<font color="Maroon" title="c3">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font>
 <b>and </b><br/><a NAME="E7:6_1"/><i><font color="Green" title="E8">A5</font></i>: 
<font color="Maroon" title="c3">G</font> is   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">Cover</a> of <font color="Maroon" title="c1">T</font>
 <b>and </b><br/><a NAME="E8:6_1"/><i><font color="Green" title="E9">A6</font></i>: 
<font color="Maroon" title="c3">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="txt" href="#E1:6_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="#E3:6_1"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="compts_1.html#D3" target="_self" title="COMPTS_1:def.3">Def3</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">G</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">G</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">G</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font> &amp; <font color="Maroon" title="c3">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> )</span><br/>

<b>thus </b><a NAME="E9:6_1"/>
( <font color="Maroon" title="c3">G</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">G</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font> &amp; <font color="Maroon" title="c3">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> )
 <b>by </b><i><a class="txt" href="#E6:6_1"><i><font color="Green" title="E7">A4</font></i></a>, <a class="txt" href="#E8:6_1"><i><font color="Green" title="E9">A6</font></i></a>, <a class="txt" href="#E7:6_1"><i><font color="Green" title="E8">A5</font></i></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>assume </b><a NAME="E2:6"/><i><font color="Green" title="E4">A7</font></i>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">T</font> is <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a></span><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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">F</font> is   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">Cover</a> of <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> implies  ex <font color="Olive" title="b1">G</font> being  <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Olive" title="b1">G</font> is   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">Cover</a> of <font color="Maroon" title="c1">T</font> &amp; <font color="Olive" title="b1">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> ) )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E3:6"/><i><font color="Green" title="E5">A8</font></i>: 
<font color="Maroon" title="c2">F</font> is   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">Cover</a> of <font color="Maroon" title="c1">T</font>
 <b>and </b><br/><a NAME="E4:6"/><i><font color="Green" title="E6">A9</font></i>: 
<font color="Maroon" title="c2">F</font> is <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">G</font> being  <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Olive" title="b1">G</font> is   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">Cover</a> of <font color="Maroon" title="c1">T</font> &amp; <font color="Olive" title="b1">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> )</span><br/>

<b>consider </b><font color="Maroon" title="c3">G</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E6:6"/><i><font color="Green" title="E7">A10</font></i>: 
<font color="Maroon" title="c3">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font>
 <b>and </b><br/><a NAME="E7:6"/><i><font color="Green" title="E8">A11</font></i>: 
<font color="Maroon" title="c3">G</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font>
 <b>and </b><br/><a NAME="E8:6"/><i><font color="Green" title="E9">A12</font></i>: 
<font color="Maroon" title="c3">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="txt" href="#E2:6"><i><font color="Green" title="E4">A7</font></i></a>, <a class="txt" href="#E3:6"><i><font color="Green" title="E5">A8</font></i></a>, <a class="txt" href="#E4:6"><i><font color="Green" title="E6">A9</font></i></a>, <a class="ref" href="compts_1.html#D7" target="_self" title="COMPTS_1:def.7">Def7</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">G</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">G</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">G</font> is   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">Cover</a> of <font color="Maroon" title="c1">T</font> &amp; <font color="Maroon" title="c3">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> )</span><br/>

<b>thus </b><a NAME="E9:6"/>
( <font color="Maroon" title="c3">G</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">G</font> is   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">Cover</a> of <font color="Maroon" title="c1">T</font> &amp; <font color="Maroon" title="c3">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> )
 <b>by </b><i><a class="txt" href="#E6:6"><i><font color="Green" title="E7">A10</font></i></a>, <a class="txt" href="#E7:6"><i><font color="Green" title="E8">A11</font></i></a>, <a class="txt" href="#E8:6"><i><font color="Green" title="E9">A12</font></i></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>
