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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</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"> (  ex <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  ex <font color="Olive" title="b2">p</font> being   <a href="waybel_1.html#V6" title="WAYBEL_1:attr.6">projection</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <font color="Olive" title="b1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <font color="Olive" title="b1">X</font></span>)</span> st <br/>( <font color="Olive" title="b2">p</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>  &amp; <font color="Maroon" title="c1">L</font>, <a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <font color="Olive" title="b2">p</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a>  ) implies <font color="Maroon" title="c1">L</font> is  <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c2">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , <font color="Maroon" title="c3">p</font> being   <a href="waybel_1.html#V6" title="WAYBEL_1:attr.6">projection</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <font color="Maroon" title="c2">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <font color="Maroon" title="c2">X</font></span>)</span><span class="kw"> such that </span><a NAME="E2:18"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
<font color="Maroon" title="c3">p</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a> 
 <span class="kw">and </span><br/><a NAME="E3:18"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
<font color="Maroon" title="c1">L</font>, <a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <font color="Maroon" title="c3">p</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</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"> <font color="Maroon" title="c1">L</font> is  <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> </span><br/>

<a NAME="E4:18"/>
 <a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <font color="Maroon" title="c3">p</font> is  <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="waybel15.html#T15" target="_self" onmouseover="rs('waybel15/T15')" onmouseout="rh()">Th15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:18"/>
<font color="Maroon" title="c1">L</font> is  <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="waybel15.html#T9" target="_self" onmouseover="rs('waybel15/T9')" onmouseout="rh()">Th9</a>, <a class="ref" href="waybel_1.html#T6" onmouseover="rs('waybel_1/T6')" onmouseout="rh()">WAYBEL_1:6</a></span>; <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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