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<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="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K5" target="_self">-SUP_category</a> </span>)</span>;<br/>

<b>assume </b><a NAME="E1:62_1"/><i><font color="Green">E43</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>



<a NAME="E2:62_1"/><i><font color="Green">E44</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="waybel34.html#E1:62_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="altcat_1.html#D4">ALTCAT_1:def 4</a></i>;<br/>
<a NAME="E3:62_1"/><b>then </b>
(  <a href="yellow21.html#K5">@</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="yellow21.html#K5">@</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp;  <a href="yellow21.html#K5">@</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="waybel34.html#E1:62_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="yellow21.html#D7">YELLOW21:def 7</a></i>;<br/>
<a NAME="E4:62_1"/><b>then </b>
(  <a href="yellow21.html#K5">@</a> <font color="Maroon">c<sub>7</sub></font> is  <a href="waybel_0.html#V18">sups-preserving</a> <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> &amp;  <a href="yellow21.html#K5">@</a> <font color="Maroon">c<sub>6</sub></font> is  <a href="waybel_0.html#V18">sups-preserving</a> <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> &amp;  <a href="yellow21.html#K5">@</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="yellow21.html#K5">@</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="yellow21.html#K5">@</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="waybel34.html#E1:62"><i><font color="Green">E40</font></i></a>, <a class="txt" href="waybel34.html#E1:62_1"><i><font color="Green">E43</font></i></a>, <a class="txt" href="waybel34.html#E2:62_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="waybel34.html#D5" target="_self">Def5</a>, <a class="ref" href="altcat_1.html#D14">ALTCAT_1:def 14</a></i>;<br/>
<a NAME="E5:62_1"/><b>then </b>
 <a href="waybel34.html#K2" target="_self">UpperAdj</a> <span class="p1">(<span class="default"><a href="yellow21.html#K5">@</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="waybel34.html#K2" target="_self">UpperAdj</a> <span class="p2">(<span class="default"><a href="yellow21.html#K5">@</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="waybel34.html#K2" target="_self">UpperAdj</a> <span class="p2">(<span class="default"><a href="yellow21.html#K5">@</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel34.html#T9" target="_self">Th9</a></i>;<br/>
<b>hence </b><a NAME="E6:62_1"/>
( <font color="Maroon">S<sub>2</sub></font>[<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>] &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>] implies <font color="Maroon">S<sub>2</sub></font>[<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>6</sub></font>] )
 <b>by </b><i><a class="ref" href="waybel20.html#T29">WAYBEL20:29</a></i>;<br/>


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