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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="lattice3.html#V1">with_suprema</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="yellow_0.html#V4" target="_self">full</a> <a href="yellow_0.html#V6" target="_self">join-inheriting</a>  <a href="yellow_0.html#M1" target="_self">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><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>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:97"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<a NAME="E2:97"/><i><font color="Green">E57</font></i>: 
 <a href="yellow_0.html#R1" target="_self">ex_sup_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="ref" href="yellow_0.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E3:97"/><b>then </b>
 <a href="yellow_0.html#K1" target="_self">"\/"</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>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="yellow_0.html#E1:97"><i><font color="Green">E56</font></i></a>, <a class="ref" href="yellow_0.html#D17" target="_self">Def17</a></i>;<br/>
<a NAME="E4:97"/><b>then </b>
(  <a href="yellow_0.html#R1" target="_self">ex_sup_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> &amp;  <a href="yellow_0.html#K1" target="_self">"\/"</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> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1" target="_self">"\/"</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>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</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> )
 
<b>by </b><i><a class="txt" href="yellow_0.html#E1:97"><i><font color="Green">E56</font></i></a>, <a class="txt" href="yellow_0.html#E2:97"><i><font color="Green">E57</font></i></a>, <a class="ref" href="yellow_0.html#T41" target="_self">Th41</a>, <a class="ref" href="yellow_0.html#T65" target="_self">Th65</a></i>;<br/>
<b>hence </b><a NAME="E5:97"/>
<font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E1:97"><i><font color="Green">E56</font></i></a>, <a class="ref" href="yellow_0.html#T41" target="_self">Th41</a></i>;<br/>


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