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<span class="kw">reconsider </span><font color="Maroon" title="c2">B</font> =  <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>  as   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">D</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>, <a class="ref" href="zfmisc_1.html#T79" title="ZFMISC_1:th.79">ZFMISC_1:79</a></span>;<br/>
<a NAME="E2:56_1_1"/>
 <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="c1">D</font>,<font color="Maroon" title="c2">B</font> #) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">D</font>
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">T</font> =  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c1">D</font>,<font color="Maroon" title="c2">B</font> #) as    <a href="simplex0.html#M1" title="SIMPLEX0:mode.1">SimplicialComplexStr</a> of <font color="Maroon" title="c1">D</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">take </span>
<font color="Maroon" title="c3">T</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c3">T</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; not <font color="Maroon" title="c3">T</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="simplex0.html#V6" title="SIMPLEX0:attr.6">total</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="simplex0.html#V4" title="SIMPLEX0:attr.4">empty-membered</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>  )</span><br/>

<a NAME="E4:56_1_1"/>
for <font color="Olive" title="b1">x</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds not <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font>
 
;<br/>
<a NAME="E5:56_1_1"/><span class="kw">then </span>
(  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c3">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">D</font> &amp; <font color="Maroon" title="c2">B</font> is  <a href="setfam_1.html#V2" title="SETFAM_1:attr.2">empty-membered</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="setfam_1.html#D11" title="SETFAM_1:def.11">SETFAM_1:def 11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:56_1_1"/>
( not <font color="Maroon" title="c3">T</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; not <font color="Maroon" title="c3">T</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="simplex0.html#V6" title="SIMPLEX0:attr.6">total</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="simplex0.html#V4" title="SIMPLEX0:attr.4">empty-membered</a>  &amp; <font color="Maroon" title="c3">T</font> is  <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="simplex0.html#D7" target="_self" title="SIMPLEX0:def.7">Def7</a>, <a class="ref" href="simplex0.html#D10" target="_self" title="SIMPLEX0:def.10">Def10</a>, <a class="ref" href="pencil_1.html#D4" title="PENCIL_1:def.4">PENCIL_1:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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