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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:31"/><i><font color="Green">E20</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #)
 <b>and </b><br/><a NAME="E2:31"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="waybel_8.html#V3" target="_self">arithmetic</a>
 ;<br/>

<a NAME="E3:31"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="waybel_8.html#V2" target="_self">algebraic</a>
 
<b>by </b><i><a class="txt" href="waybel_8.html#E2:31"><i><font color="Green">E21</font></i></a>, <a class="ref" href="waybel_8.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E4:31"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel_8.html#V2" target="_self">algebraic</a>
 
<b>by </b><i><a class="txt" href="waybel_8.html#E1:31"><i><font color="Green">E20</font></i></a>, <a class="ref" href="waybel_8.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E5:31"/><i><font color="Green">E24</font></i>: 
 <a href="waybel_8.html#K1" target="_self">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font> is <a href="yellow_0.html#V5">meet-inheriting</a>
 
<b>by </b><i><a class="txt" href="waybel_8.html#E2:31"><i><font color="Green">E21</font></i></a>, <a class="ref" href="waybel_8.html#D5" target="_self">Def5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="waybel_8.html#E1:31"><i><font color="Green">E20</font></i></a></i>;<br/><b>assume </b><b>that </b><br/><a NAME="E2:31_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" target="_self">CompactSublatt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E3:31_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" target="_self">CompactSublatt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:31_1"/><i><font color="Green">E27</font></i>: 
 <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E5:31_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel_0.html#V24">up-complete</a>
 <b>by </b><i><a class="txt" href="waybel_8.html#E4:31"><i><font color="Green">E23</font></i></a>, <a class="ref" href="waybel_8.html#D4" target="_self">Def4</a></i>;<br/><a NAME="E6:31_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="waybel_0.html#V24">up-complete</a>
 <b>by </b><i><a class="txt" href="waybel_8.html#E3:31"><i><font color="Green">E22</font></i></a>, <a class="ref" href="waybel_8.html#D4" target="_self">Def4</a></i>;<br/><a NAME="E7:31_1"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="waybel_3.html#V1">compact</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="waybel_3.html#V1">compact</a> )
 <b>by </b><i><a class="txt" href="waybel_8.html#E2:31_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="waybel_8.html#E3:31_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="waybel_8.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E8:31_1"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> is <a href="waybel_3.html#V1">compact</a> &amp; <font color="Maroon">c<sub>6</sub></font> is <a href="waybel_3.html#V1">compact</a> )
 <b>by </b><i><a class="txt" href="waybel_8.html#E1:31"><i><font color="Green">E20</font></i></a>, <a class="txt" href="waybel_8.html#E5:31_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="waybel_8.html#T9" target="_self">Th9</a></i>;<br/><a NAME="E9:31_1"/><b>then </b><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" target="_self">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" target="_self">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="waybel_8.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E10:31_1"/>
 <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="waybel_8.html#E1:31"><i><font color="Green">E20</font></i></a>, <a class="txt" href="waybel_8.html#E4:31_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="yellow_0.html#T14">YELLOW_0:14</a></i>;<br/><a NAME="E11:31_1"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" target="_self">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="waybel_8.html#E5:31"><i><font color="Green">E24</font></i></a>, <a class="txt" href="waybel_8.html#E9:31_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="yellow_0.html#D16">YELLOW_0:def 16</a></i>;<br/><a NAME="E12:31_1"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="domain_1.html#K7">}</a></span> is <a href="waybel_3.html#V1">compact</a>
 <b>by </b><i><a class="ref" href="waybel_8.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E13:31_1"/>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span>
 <b>by </b><i><a class="txt" href="waybel_8.html#E1:31"><i><font color="Green">E20</font></i></a>, <a class="txt" href="waybel_8.html#E4:31_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="yellow_0.html#T27">YELLOW_0:27</a></i>;<br/><a NAME="E14:31_1"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span> is <a href="waybel_3.html#V1">compact</a>
 <b>by </b><i><a class="txt" href="waybel_8.html#E1:31"><i><font color="Green">E20</font></i></a>, <a class="txt" href="waybel_8.html#E6:31_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="waybel_8.html#E12:31_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="waybel_8.html#T9" target="_self">Th9</a></i>;<br/><b>hence </b><a NAME="E15:31_1"/>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" target="_self">CompactSublatt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel_8.html#D1" target="_self">Def1</a></i>;<br/></div><b>end;</b></div>
<a NAME="E7:31"/><b>then </b>
 <a href="waybel_8.html#K1" target="_self">CompactSublatt</a> <font color="Maroon">c<sub>2</sub></font> is <a href="yellow_0.html#V5">meet-inheriting</a>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D16">YELLOW_0:def 16</a></i>;<br/>
<b>hence </b><a NAME="E8:31"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel_8.html#V3" target="_self">arithmetic</a>
 <b>by </b><i><a class="txt" href="waybel_8.html#E4:31"><i><font color="Green">E23</font></i></a>, <a class="ref" href="waybel_8.html#D5" target="_self">Def5</a></i>;<br/>


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