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<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="conlat_1.html#NM1" title="CONLAT_1:NM.1">FormalContext</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="conlat_2.html#K3" title="CONLAT_2:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#K6" title="CONLAT_1:func.6">Concept-with-all-Attributes</a> <font color="Maroon" title="c1">C</font> &amp;  <a href="conlat_2.html#K2" title="CONLAT_2:func.2">"/\"</a> <span class="p1">(<span class="default"><a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font> )</span><br/>

<a NAME="E1:8"/><i><font color="Green" title="E5">A1</font></i>: 
 <a href="conlat_2.html#K3" title="CONLAT_2:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T50" title="LATTICE3:th.50">LATTICE3:50</a></i>;<br/>
<a NAME="E2:8"/>
for <font color="Olive" title="b1">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span>  st <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/> <a href="conlat_2.html#K1" title="CONLAT_2:func.1">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Olive" title="b1">q</font>
 
;<br/>
<a NAME="E3:8"/><b>then </b><i><font color="Green" title="E6">A2</font></i>: 
 <a href="conlat_2.html#K1" title="CONLAT_2:func.1">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="lattice3.html#R3" title="LATTICE3:pred.3">is_less_than</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="lattice3.html#D16" title="LATTICE3:def.16">LATTICE3:def 16</a></i>;<br/>
<a NAME="E4:8"/>
for <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span>  st <font color="Olive" title="b1">b</font> <a href="lattice3.html#R3" title="LATTICE3:pred.3">is_less_than</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/><font color="Olive" title="b1">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="conlat_2.html#K1" title="CONLAT_2:func.1">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">b</font> <a href="lattice3.html#R3" title="LATTICE3:pred.3">is_less_than</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <font color="Maroon" title="c2">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="conlat_2.html#K1" title="CONLAT_2:func.1">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:8_1"/>
<font color="Maroon" title="c2">b</font> <a href="lattice3.html#R3" title="LATTICE3:pred.3">is_less_than</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="conlat_2.html#K1" title="CONLAT_2:func.1">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span></span><br/>

<a NAME="E2:8_1"/><i><font color="Green" title="E7">A3</font></i>: 
<font color="Maroon" title="c2">b</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a>  <a href="conlat_1.html#R2" title="CONLAT_1:pred.2">is-SubConcept-of</a>  <a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="conlat_1.html#T34" title="CONLAT_1:th.34">CONLAT_1:34</a></i>;<br/>
<a NAME="E3:8_1"/>
 <a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K1" title="CONLAT_2:func.1">@</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#D24" title="CONLAT_1:def.24">CONLAT_1:def 24</a></i>;<br/>
<b>hence </b><a NAME="E4:8_1"/>
<font color="Maroon" title="c2">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="conlat_2.html#K1" title="CONLAT_2:func.1">@</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:8_1"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="conlat_1.html#T47" title="CONLAT_1:th.47">CONLAT_1:47</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:8"/>
(  <a href="conlat_2.html#K3" title="CONLAT_2:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#K6" title="CONLAT_1:func.6">Concept-with-all-Attributes</a> <font color="Maroon" title="c1">C</font> &amp;  <a href="conlat_2.html#K2" title="CONLAT_2:func.2">"/\"</a> <span class="p1">(<span class="default"><a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p2">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font> )
 <b>by </b><i><a class="txt" href="#E1:8"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="#E3:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="conlat_2.html#T1" target="_self" title="CONLAT_2:th.1">Th1</a>, <a class="ref" href="lattice3.html#T34" title="LATTICE3:th.34">LATTICE3:34</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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