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<span class="kw">set </span><font color="Maroon" title="c3">T</font> =  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>,<span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a></span>)</span></span>)</span> #);<br/>
<a NAME="E1:80_1_1"/>
(  <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>(# <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>,<span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a></span>)</span></span>)</span> #) is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp;  <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>(# <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>,<span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a></span>)</span></span>)</span> #) <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#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">T</font> =  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>,<span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a></span>)</span></span>)</span> #) as   <a href="simplex0.html#NM4" title="SIMPLEX0:NM.4">SimplicialComplex</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>, <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/>
<span class="kw">take </span>
<font color="Maroon" title="c4">T</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="c4">T</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 <font color="Maroon" title="c4">T</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><br/>

<span class="kw">thus </span><a NAME="E3:80_1_1"/>
(  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c4">T</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 <font color="Maroon" title="c4">T</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#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></span>; <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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