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<b>let </b><font color="Maroon" title="c1">X</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"> for <font color="Olive" title="b1">Y</font> being   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b3">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">Y</font>  st <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">B</font> holds <br/>( <font color="Olive" title="b2">A</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> iff <font color="Olive" title="b3">B</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">Y</font> be    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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 <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y</font>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">B</font> holds <br/>( <font color="Olive" title="b1">A</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> iff <font color="Olive" title="b2">B</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> )</span><br/><b>let </b><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y</font>  st <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">B</font> holds <br/>( <font color="Maroon" title="c3">A</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> iff <font color="Olive" title="b1">B</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> )</span><br/><b>let </b><font color="Maroon" title="c4">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y</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">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> implies ( <font color="Maroon" title="c3">A</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> iff <font color="Maroon" title="c4">B</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> ) )</span><br/>







<b>assume </b><a NAME="E1:39"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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="c3">A</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> iff <font color="Maroon" title="c4">B</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> )</span><br/>

<a NAME="E2:39"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c4">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">Y</font>
 
;<br/>
<b>hence </b><a NAME="E3:39"/>
( <font color="Maroon" title="c3">A</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> implies <font color="Maroon" title="c4">B</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> )
 <b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="compts_1.html#T11" target="_self" title="COMPTS_1:th.11">Th11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">B</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> implies <font color="Maroon" title="c3">A</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> )</span><br/>

<b>assume </b><a NAME="E4:39"/>
<font color="Maroon" title="c4">B</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="c3">A</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a></span><br/>

<a NAME="E5:39"/><b>then </b>
for <font color="Olive" title="b1">P</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y</font>  st <font color="Olive" title="b1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> holds <br/><font color="Olive" title="b1">P</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>
 
<b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:39"/>
<font color="Maroon" title="c3">A</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>
 <b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E2:39"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="compts_1.html#T11" target="_self" title="COMPTS_1:th.11">Th11</a></i>; <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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