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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K9" title="WAYBEL10:func.9">Subalgebras</a> <font color="Maroon" title="c1">L</font></span>)</span> iff <font color="Olive" title="b1">x</font> is   <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>   <a href="waybel10.html#NV1" title="WAYBEL10:NV.1">closure</a>   <a href="waybel_0.html#V4" title="WAYBEL_0:attr.4">directed-sups-inheriting</a>  <a href="waybel10.html#NM1" title="WAYBEL10:NM.1">System</a> of <font color="Maroon" title="c1">L</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <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"> ( <font color="Maroon" title="c2">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K9" title="WAYBEL10:func.9">Subalgebras</a> <font color="Maroon" title="c1">L</font></span>)</span> iff <font color="Maroon" title="c2">x</font> is   <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>   <a href="waybel10.html#NV1" title="WAYBEL10:NV.1">closure</a>   <a href="waybel_0.html#V4" title="WAYBEL_0:attr.4">directed-sups-inheriting</a>  <a href="waybel10.html#NM1" title="WAYBEL10:NM.1">System</a> of <font color="Maroon" title="c1">L</font> )</span><br/>



<a NAME="E1:61"/>
( <font color="Maroon" title="c2">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K5" title="WAYBEL10:func.5">ClosureSystems</a> <font color="Maroon" title="c1">L</font></span>)</span> iff <font color="Maroon" title="c2">x</font> is   <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>   <a href="waybel10.html#NV1" title="WAYBEL10:NV.1">closure</a>  <a href="waybel10.html#NM1" title="WAYBEL10:NM.1">System</a> of <font color="Maroon" title="c1">L</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel10.html#T17" target="_self" title="WAYBEL10:th.17">Th17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:61"/>
( <font color="Maroon" title="c2">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K9" title="WAYBEL10:func.9">Subalgebras</a> <font color="Maroon" title="c1">L</font></span>)</span> iff <font color="Maroon" title="c2">x</font> is   <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>   <a href="waybel10.html#NV1" title="WAYBEL10:NV.1">closure</a>   <a href="waybel_0.html#V4" title="WAYBEL_0:attr.4">directed-sups-inheriting</a>  <a href="waybel10.html#NM1" title="WAYBEL10:NM.1">System</a> of <font color="Maroon" title="c1">L</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel10.html#D8" target="_self" title="WAYBEL10:def.8">Def8</a>, <a class="ref" href="yellow_0.html#T59" title="YELLOW_0:th.59">YELLOW_0:59</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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