<?xml version="1.0"?>
<div class="add">

<b>thus </b><a NAME="E1:83_1_1"/>
<span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span> is <a href="waybel_8.html#V2" title="WAYBEL_8:attr.2">algebraic</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_8.html#D5" title="WAYBEL_8:def.5">WAYBEL_8:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span> is <a href="yellow_0.html#V5" title="YELLOW_0:attr.5">meet-inheriting</a></span><br/>

<b>set </b><font color="Maroon" title="c3">C</font> =  <a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span>;<br/>
<b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D16" title="YELLOW_0:def.16">YELLOW_0:def 16</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p2"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span></span>)</span> or  not <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p2"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span></span>)</span> or  not  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span> or  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p2"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span></span>)</span> )</span><br/>

<b>assume </b><a NAME="E2:83_1_1"/><i><font color="Green" title="E30">A1</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p2"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span></span>)</span> &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p2"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span></span>)</span> &amp;  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p2"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span></span>)</span></span><br/>

<a NAME="E3:83_1_1"/><i><font color="Green" title="E31">A2</font></i>: 
(  <a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c1">S</font> is <a href="yellow_0.html#V5" title="YELLOW_0:attr.5">meet-inheriting</a> &amp;  <a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">T</font> is <a href="yellow_0.html#V5" title="YELLOW_0:attr.5">meet-inheriting</a> )
 
<b>by </b><i><a class="ref" href="waybel_8.html#D5" title="WAYBEL_8:def.5">WAYBEL_8:def 5</a></i>;<br/>
<a NAME="E4:83_1_1"/><i><font color="Green" title="E32">A3</font></i>: 
(  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> </span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">S</font> &amp;  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> </span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">T</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T21" title="YELLOW_0:th.21">YELLOW_0:21</a></i>;<br/>
<a NAME="E5:83_1_1"/>
( <font color="Maroon" title="c4">x</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> &amp; <font color="Maroon" title="c5">y</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> )
 
<b>by </b><i><a class="txt" href="#E2:83_1_1"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="waybel_8.html#D1" title="WAYBEL_8:def.1">WAYBEL_8:def 1</a></i>;<br/>
<a NAME="E6:83_1_1"/><b>then </b>
( <font color="Maroon" title="c4">x</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a>  is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> &amp; <font color="Maroon" title="c5">y</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a>  is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> &amp; <font color="Maroon" title="c4">x</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a>  is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> &amp; <font color="Maroon" title="c5">y</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a>  is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> )
 
<b>by </b><i><a class="ref" href="yellow10.html#T22" target="_self" title="YELLOW10:th.22">Th22</a></i>;<br/>
<a NAME="E7:83_1_1"/><b>then </b>
( <font color="Maroon" title="c4">x</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c1">S</font></span>)</span> &amp; <font color="Maroon" title="c5">y</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c1">S</font></span>)</span> &amp; <font color="Maroon" title="c4">x</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">T</font></span>)</span> &amp; <font color="Maroon" title="c5">y</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">T</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="waybel_8.html#D1" title="WAYBEL_8:def.1">WAYBEL_8:def 1</a></i>;<br/>
<a NAME="E8:83_1_1"/><b>then </b>
(  <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> </span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c1">S</font></span>)</span> &amp;  <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> </span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">T</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="#E3:83_1_1"><i><font color="Green" title="E31">A2</font></i></a>, <a class="txt" href="#E4:83_1_1"><i><font color="Green" title="E32">A3</font></i></a>, <a class="ref" href="yellow_0.html#D16" title="YELLOW_0:def.16">YELLOW_0:def 16</a></i>;<br/>
<a NAME="E9:83_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> </span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c1">S</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> </span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">T</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/>
<a NAME="E10:83_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> </span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> </span>)</span> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> </span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> </span>)</span> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> )
 
<b>by </b><i><a class="ref" href="waybel_8.html#D1" title="WAYBEL_8:def.1">WAYBEL_8:def 1</a></i>;<br/>
<a NAME="E11:83_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a>  is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a>  is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> )
 
<b>by </b><i><a class="ref" href="yellow10.html#T13" target="_self" title="YELLOW10:th.13">Th13</a></i>;<br/>
<a NAME="E12:83_1_1"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">y</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a>
 
<b>by </b><i><a class="ref" href="yellow10.html#T23" target="_self" title="YELLOW10:th.23">Th23</a></i>;<br/>
<a NAME="E13:83_1_1"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/>
<b>hence </b><a NAME="E14:83_1_1"/>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p2"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="waybel_8.html#D1" title="WAYBEL_8:def.1">WAYBEL_8:def 1</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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