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<span class="kw">take </span><font color="Maroon" title="c1">T</font> = the  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>   <a href="matroid0.html#V1" title="MATROID0:attr.1">subset-closed</a>   <a href="simplex0.html#V2" title="SIMPLEX0:attr.2">finite-vertices</a>   <a href="simplex0.html#NV9" title="SIMPLEX0:NV.9">with_non-empty_element</a>   <a href="simplex0.html#NV10" title="SIMPLEX0:NV.10">with_empty_element</a>   <a href="simplex0.html#M1" title="SIMPLEX0:mode.1">SimplicialComplexStr</a> of the  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> ; <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="c1">T</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; not <font color="Maroon" title="c1">T</font> is  <a href="simplex0.html#V5" title="SIMPLEX0:attr.5">with_non-empty_elements</a>  &amp; not <font color="Maroon" title="c1">T</font> is  <a href="simplex0.html#V4" title="SIMPLEX0:attr.4">empty-membered</a>  &amp; <font color="Maroon" title="c1">T</font> is  <a href="simplex0.html#V2" title="SIMPLEX0:attr.2">finite-vertices</a>  &amp; <font color="Maroon" title="c1">T</font> is  <a href="matroid0.html#V1" title="MATROID0:attr.1">subset-closed</a>  &amp; <font color="Maroon" title="c1">T</font> is  <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:57_1_1"/>
( not <font color="Maroon" title="c1">T</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; not <font color="Maroon" title="c1">T</font> is  <a href="simplex0.html#V5" title="SIMPLEX0:attr.5">with_non-empty_elements</a>  &amp; not <font color="Maroon" title="c1">T</font> is  <a href="simplex0.html#V4" title="SIMPLEX0:attr.4">empty-membered</a>  &amp; <font color="Maroon" title="c1">T</font> is  <a href="simplex0.html#V2" title="SIMPLEX0:attr.2">finite-vertices</a>  &amp; <font color="Maroon" title="c1">T</font> is  <a href="matroid0.html#V1" title="MATROID0:attr.1">subset-closed</a>  &amp; <font color="Maroon" title="c1">T</font> is  <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>  )
 ; <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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