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<a NAME="E1:98_1_1"/>
 <a href="matroid0.html#K1" title="MATROID0:func.1">the_family_of</a> <font color="Maroon" title="c2">KX</font> is  <a href="classes1.html#V1" title="CLASSES1:attr.1">subset-closed</a> 
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">BA</font> = <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">KX</font> as   <a href="classes1.html#V1" title="CLASSES1:attr.1">subset-closed</a>   <a href="lexbfs.html#V1" title="LEXBFS:attr.1">finite-membered</a>  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c3">A</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:98"><span class="lab"><font color="Green" title="E41">A1</font></span></a>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">KA</font> =  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">BA</font> #);<br/>
<a NAME="E3:98_1_1"/><span class="lab"><font color="Green" title="E42">A2</font></span>: 
(  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">BA</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">KX</font> &amp;  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">BA</font> #) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">KX</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></span>;<br/>
<a NAME="E4:98_1_1"/>
<font color="Maroon" title="c4">BA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matroid0.html#K1" title="MATROID0:func.1">the_family_of</a> <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">BA</font> #)
 
;<br/>
<a NAME="E5:98_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A3</font></span>: 
(  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">BA</font> #) is  <a href="matroid0.html#V1" title="MATROID0:attr.1">subset-closed</a>  &amp;  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">BA</font> #) is  <a href="matroid0.html#V3" title="MATROID0:attr.3">finite-membered</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matroid0.html#D3" title="MATROID0:def.3">MATROID0:def 3</a>, <a class="ref" href="matroid0.html#D6" title="MATROID0:def.6">MATROID0:def 6</a></span>;<br/>
<a NAME="E6:98_1_1"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">KX</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="simplex0.html#D9" target="_self" title="SIMPLEX0:def.9">Def9</a></span>;<br/>
<a NAME="E7:98_1_1"/><span class="kw">then </span>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">BA</font> #) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E8:98_1_1"/><span class="kw">then </span>
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">BA</font> #) is    <a href="simplex0.html#M1" title="SIMPLEX0:mode.1">SimplicialComplexStr</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="simplex0.html#D9" target="_self" title="SIMPLEX0:def.9">Def9</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">KA</font> =  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">BA</font> #) as   <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>   <a href="simplex0.html#V7" title="SIMPLEX0:attr.7">maximal</a>   <a href="simplex0.html#M2" title="SIMPLEX0:mode.2">SubSimplicialComplex</a> of <font color="Maroon" title="c2">KX</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:98_1_1"><span class="lab"><font color="Green" title="E42">A2</font></span></a>, <a class="txt" href="#E5:98_1_1"><span class="lab"><font color="Green" title="E43">A3</font></span></a>, <a class="ref" href="simplex0.html#D13" target="_self" title="SIMPLEX0:def.13">Def13</a>, <a class="ref" href="simplex0.html#T33" target="_self" title="SIMPLEX0:th.33">Th33</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c6">KA</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c6">KA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font></span><br/>

<span class="kw">thus </span><a NAME="E10:98_1_1"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c6">KA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font>
 ; <a class="txt" 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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