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<b>let </b><font color="Maroon" title="c1">V1</font>, <font color="Maroon" title="c2">V2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="abcmiz_1.html#K49" title="ABCMIZ_1:func.49">VarPoset</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">V1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c2">V2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">V1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">V2</font> &amp; <font color="Maroon" title="c1">V1</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">V2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">V1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">V2</font> )</span><br/>

<b>set </b><font color="Maroon" title="c3">V</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="abcmiz_1.html#K1" title="ABCMIZ_1:func.1">varcl</a> <font color="Olive" title="b1">A</font></span>)</span> where <font color="Olive" title="b1">A</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>  : verum </span>}</span> ;<br/>
<b>consider </b><font color="Maroon" title="c4">A0</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a> ;<br/>
<a NAME="E2:202"/>
 <a href="abcmiz_1.html#K1" title="ABCMIZ_1:func.1">varcl</a> <font color="Maroon" title="c4">A0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="abcmiz_1.html#K1" title="ABCMIZ_1:func.1">varcl</a> <font color="Olive" title="b1">A</font></span>)</span> where <font color="Olive" title="b1">A</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>  : verum </span>}</span> 
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">V</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="abcmiz_1.html#K1" title="ABCMIZ_1:func.1">varcl</a> <font color="Olive" title="b1">A</font></span>)</span> where <font color="Olive" title="b1">A</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>  : verum </span>}</span>  as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<a NAME="E4:202"/><i><font color="Green" title="E99">A1</font></i>: 
 <a href="abcmiz_1.html#K49" title="ABCMIZ_1:func.49">VarPoset</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <font color="Maroon" title="c5">V</font></span>)</span> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a> 
 
;<br/>
<a NAME="E5:202"/><i><font color="Green" title="E100">A2</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <font color="Maroon" title="c5">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">V</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T1" title="YELLOW_1:th.1">YELLOW_1:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">v1</font> = <font color="Maroon" title="c1">V1</font>, <font color="Maroon" title="c7">v2</font> = <font color="Maroon" title="c2">V2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <font color="Maroon" title="c5">V</font></span>)</span> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a> </span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">a1</font> = <font color="Maroon" title="c1">V1</font>, <font color="Maroon" title="c9">a2</font> = <font color="Maroon" title="c2">V2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <font color="Maroon" title="c5">V</font></span>)</span> ;<br/>
<a NAME="E8:202"/>
<font color="Maroon" title="c1">V1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">V</font>
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E5:202"><i><font color="Green" title="E100">A2</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c10">A1</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a> <b> such that </b><br/><a NAME="E10:202"/><i><font color="Green" title="E101">A4</font></i>: 
<font color="Maroon" title="c1">V1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K1" title="ABCMIZ_1:func.1">varcl</a> <font color="Maroon" title="c10">A1</font>
 ;<br/>
<a NAME="E11:202"/>
<font color="Maroon" title="c2">V2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">V</font>
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E5:202"><i><font color="Green" title="E100">A2</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c11">A2</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a> <b> such that </b><br/><a NAME="E13:202"/><i><font color="Green" title="E102">A5</font></i>: 
<font color="Maroon" title="c2">V2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K1" title="ABCMIZ_1:func.1">varcl</a> <font color="Maroon" title="c11">A2</font>
 ;<br/>
<a NAME="E14:202"/><i><font color="Green" title="E103">A6</font></i>: 
( <font color="Maroon" title="c8">a1</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> &amp; <font color="Maroon" title="c9">a2</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v2</font> )
 
;<br/>
<a NAME="E15:202"/><i><font color="Green" title="E104">A7</font></i>: 
(  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <font color="Maroon" title="c5">V</font> is <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a> &amp;  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <font color="Maroon" title="c5">V</font> is <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> )
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E4:202"><i><font color="Green" title="E99">A1</font></i></a>, <a class="ref" href="lattice3.html#T10" title="LATTICE3:th.10">LATTICE3:10</a>, <a class="ref" href="yellow_7.html#T16" title="YELLOW_7:th.16">YELLOW_7:16</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">x1</font> = <font color="Maroon" title="c1">V1</font>, <font color="Maroon" title="c13">x2</font> = <font color="Maroon" title="c2">V2</font> as  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>  <b>by </b><i><a class="txt" href="abcmiz_1.html#E10:202"><i><font color="Green" title="E101">A4</font></i></a>, <a class="txt" href="abcmiz_1.html#E13:202"><i><font color="Green" title="E102">A5</font></i></a>, <a class="ref" href="abcmiz_1.html#T24" target="_self" title="ABCMIZ_1:th.24">Th18</a></i>;<br/>
<a NAME="E17:202"/>
<font color="Maroon" title="c1">V1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">V2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K1" title="ABCMIZ_1:func.1">varcl</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">x1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c13">x2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E10:202"><i><font color="Green" title="E101">A4</font></i></a>, <a class="txt" href="abcmiz_1.html#E13:202"><i><font color="Green" title="E102">A5</font></i></a>, <a class="ref" href="abcmiz_1.html#T13" target="_self" title="ABCMIZ_1:th.13">Th9</a></i>;<br/>
<a NAME="E18:202"/><b>then </b>
<font color="Maroon" title="c1">V1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">V2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">V</font>
 
;<br/>
<a NAME="E19:202"/><b>then </b>
<font color="Maroon" title="c8">a1</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Maroon" title="c9">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">V1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">V2</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T9" title="YELLOW_1:th.9">YELLOW_1:9</a></i>;<br/>
<b>hence </b><a NAME="E20:202"/>
<font color="Maroon" title="c1">V1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c2">V2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">V1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">V2</font>
 <b>by </b><i><a class="txt" href="abcmiz_1.html#E14:202"><i><font color="Green" title="E103">A6</font></i></a>, <a class="txt" href="abcmiz_1.html#E15:202"><i><font color="Green" title="E104">A7</font></i></a>, <a class="ref" href="yellow_7.html#T21" title="YELLOW_7:th.21">YELLOW_7:21</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">V1</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">V2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">V1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">V2</font></span><br/>

<a NAME="E21:202"/>
<font color="Maroon" title="c1">V1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">V2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K1" title="ABCMIZ_1:func.1">varcl</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">A1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c11">A2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E10:202"><i><font color="Green" title="E101">A4</font></i></a>, <a class="txt" href="abcmiz_1.html#E13:202"><i><font color="Green" title="E102">A5</font></i></a>, <a class="ref" href="abcmiz_1.html#T11" target="_self" title="ABCMIZ_1:th.11">Th10</a></i>;<br/>
<a NAME="E22:202"/><b>then </b>
<font color="Maroon" title="c8">a1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c9">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">V</font>
 
;<br/>
<a NAME="E23:202"/><b>then </b>
<font color="Maroon" title="c8">a1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c9">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">V1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">V2</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T8" title="YELLOW_1:th.8">YELLOW_1:8</a></i>;<br/>
<b>hence </b><a NAME="E24:202"/>
<font color="Maroon" title="c1">V1</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">V2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">V1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">V2</font>
 <b>by </b><i><a class="txt" href="abcmiz_1.html#E14:202"><i><font color="Green" title="E103">A6</font></i></a>, <a class="txt" href="abcmiz_1.html#E15:202"><i><font color="Green" title="E104">A7</font></i></a>, <a class="ref" href="yellow_7.html#T23" title="YELLOW_7:th.23">YELLOW_7:23</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>
