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<span class="kw">set </span><font color="Maroon" title="c2">v</font> = the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font>;<br/>
<span class="kw">take </span><font color="Maroon" title="c3">C</font> =  <a href="simplex0.html#K5" title="SIMPLEX0:func.5">Complex_of</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>; <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">C</font> is  <a href="simplex0.html#V4" title="SIMPLEX0:attr.4">empty-membered</a>  &amp; <font color="Maroon" title="c3">C</font> is  <a href="simplex0.html#V2" title="SIMPLEX0:attr.2">finite-vertices</a>  &amp; <font color="Maroon" title="c3">C</font> is  <a href="simplex1.html#V1" title="SIMPLEX1:attr.1">affinely-independent</a>  &amp; <font color="Maroon" title="c3">C</font> is  <a href="simplex1.html#V2" title="SIMPLEX1:attr.2">simplex-join-closed</a>  &amp; <font color="Maroon" title="c3">C</font> is  <a href="simplex0.html#V6" title="SIMPLEX0:attr.6">total</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:44_1_1"/>
( not <font color="Maroon" title="c3">C</font> is  <a href="simplex0.html#V4" title="SIMPLEX0:attr.4">empty-membered</a>  &amp; <font color="Maroon" title="c3">C</font> is  <a href="simplex0.html#V2" title="SIMPLEX0:attr.2">finite-vertices</a>  &amp; <font color="Maroon" title="c3">C</font> is  <a href="simplex1.html#V1" title="SIMPLEX1:attr.1">affinely-independent</a>  &amp; <font color="Maroon" title="c3">C</font> is  <a href="simplex1.html#V2" title="SIMPLEX1:attr.2">simplex-join-closed</a>  &amp; <font color="Maroon" title="c3">C</font> is  <a href="simplex0.html#V6" title="SIMPLEX0:attr.6">total</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="simplex0.html#D7" title="SIMPLEX0:def.7">SIMPLEX0:def 7</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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