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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</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">S</font> being  <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> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel10.html#K6" title="WAYBEL10:func.6">ClImageMap</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel10.html#K7" title="WAYBEL10:func.7">closure_op</a> <font color="Olive" title="b1">S</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>   <a href="yellow_0.html#V7" title="YELLOW_0:attr.7">infs-inheriting</a>   <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel10.html#K6" title="WAYBEL10:func.6">ClImageMap</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel10.html#K7" title="WAYBEL10:func.7">closure_op</a> <font color="Maroon" title="c2">S</font></span><br/>



<a NAME="E1:50"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
 <a href="waybel10.html#K7" title="WAYBEL10:func.7">closure_op</a> <font color="Maroon" title="c2">S</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#K3" title="WAYBEL10:func.3">ClOpers</a> <font color="Maroon" title="c1">L</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel10.html#T11" target="_self" title="WAYBEL10:th.11">Th11</a></span>;<br/>
<span class="p1">(<span class="default"><a href="waybel10.html#K6" title="WAYBEL10:func.6">ClImageMap</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="waybel10.html#K7" title="WAYBEL10:func.7">closure_op</a> <font color="Maroon" title="c2">S</font></span>)</span> = 
 <a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p1">(<span class="default"><a href="waybel10.html#K7" title="WAYBEL10:func.7">closure_op</a> <font color="Maroon" title="c2">S</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel10.html#D5" target="_self" title="WAYBEL10:def.5">Def5</a></span>
<br/>.= 
<font color="Maroon" title="c2">S</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel10.html#T19" target="_self" title="WAYBEL10:th.19">Th19</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:50"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel10.html#K6" title="WAYBEL10:func.6">ClImageMap</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel10.html#K7" title="WAYBEL10:func.7">closure_op</a> <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</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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