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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V1">with_suprema</a> <a href="lattice3.html#V2">with_infima</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V1">with_suprema</a> <a href="lattice3.html#V2">with_infima</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>



<b>assume </b><a NAME="E1:73"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span> holds <font color="Olive">b<sub>1</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">b<sub>3</sub></font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D3">WAYBEL_1:def 3</a><br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D3">WAYBEL_1:def 3</a><br/>

<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E3:73"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 
;<br/>
<a NAME="E4:73"/><b>then </b><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T24">YELLOW_0:24</a>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="yellow_3.html#K8">`1</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="lattice3.html#K12">"/\"</a> <span class="p2"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K7">]</a></span></span>)</span> <a href="yellow_3.html#K8">`1</a> 
<b>by </b><i><a class="txt" href="yellow10.html#E4:73"><i><font color="Green">E30</font></i></a>, <a class="ref" href="yellow10.html#T15" target="_self">Th15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="lattice3.html#K13">"\/"</a> <span class="p3"><a href="yellow_3.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="yellow_3.html#K7">]</a></span></span>)</span></span>)</span> <a href="yellow_3.html#K8">`1</a> 
<b>by </b><i><a class="txt" href="yellow10.html#E4:73"><i><font color="Green">E30</font></i></a>, <a class="ref" href="yellow10.html#T16" target="_self">Th16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="lattice3.html#K12">"/\"</a> <span class="p3"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K7">]</a></span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="lattice3.html#K12">"/\"</a> <span class="p3"><a href="yellow_3.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="yellow_3.html#K7">]</a></span></span>)</span></span>)</span> <a href="yellow_3.html#K8">`1</a> 
<b>by </b><i><a class="txt" href="yellow10.html#E1:73"><i><font color="Green">E29</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="lattice3.html#K12">"/\"</a> <span class="p3"><a href="yellow_3.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="yellow_3.html#K7">]</a></span></span>)</span></span>)</span> <a href="yellow_3.html#K8">`1</a> 
<b>by </b><i><a class="txt" href="yellow10.html#E4:73"><i><font color="Green">E30</font></i></a>, <a class="ref" href="yellow10.html#T15" target="_self">Th15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="lattice3.html#K13">"\/"</a> <span class="p2"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K7">]</a></span></span>)</span> <a href="yellow_3.html#K8">`1</a> 
<b>by </b><i><a class="txt" href="yellow10.html#E4:73"><i><font color="Green">E30</font></i></a>, <a class="ref" href="yellow10.html#T15" target="_self">Th15</a></i>
<br/>.= 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="yellow_3.html#K8">`1</a> 
<b>by </b><i><a class="txt" href="yellow10.html#E4:73"><i><font color="Green">E30</font></i></a>, <a class="ref" href="yellow10.html#T16" target="_self">Th16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
;<br/>


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