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<span class="kw">take </span>
 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#M2" title="HIDDEN:mode.2">set</a> 
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  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#M2" title="HIDDEN:mode.2">set</a>  is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  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#M2" title="HIDDEN:mode.2">set</a>  is  <a href="simplex0.html#NV10" title="SIMPLEX0:NV.10">with_empty_element</a>  &amp;  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#M2" title="HIDDEN:mode.2">set</a>  is  <a href="simplex0.html#NV9" title="SIMPLEX0:NV.9">with_non-empty_element</a>  &amp;  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#M2" title="HIDDEN:mode.2">set</a>  is  <a href="simplex0.html#V2" title="SIMPLEX0:attr.2">finite-vertices</a>  &amp;  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#M2" title="HIDDEN:mode.2">set</a>  is  <a href="matroid0.html#V1" title="MATROID0:attr.1">subset-closed</a>  &amp;  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#M2" title="HIDDEN:mode.2">set</a>  is  <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:52_1_1"/>
(  not  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#M2" title="HIDDEN:mode.2">set</a>  is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  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#M2" title="HIDDEN:mode.2">set</a>  is  <a href="simplex0.html#NV10" title="SIMPLEX0:NV.10">with_empty_element</a>  &amp;  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#M2" title="HIDDEN:mode.2">set</a>  is  <a href="simplex0.html#NV9" title="SIMPLEX0:NV.9">with_non-empty_element</a>  &amp;  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#M2" title="HIDDEN:mode.2">set</a>  is  <a href="simplex0.html#V2" title="SIMPLEX0:attr.2">finite-vertices</a>  &amp;  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#M2" title="HIDDEN:mode.2">set</a>  is  <a href="matroid0.html#V1" title="MATROID0:attr.1">subset-closed</a>  &amp;  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#M2" title="HIDDEN:mode.2">set</a>  is  <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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