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<a NAME="E1:19_1"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="waybel_0.html#NM8">LATTICE</a>  st <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/>for <font color="Olive">f</font> being  <a href="struct_0.html#NM6">Function</a> of <font color="Olive">a</font>,<font color="Olive">b</font><br/> for <font color="Olive">g</font> being  <a href="struct_0.html#NM6">Function</a> of <font color="Olive">b</font>,<font color="Olive">c</font>  st <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">a</font>,<font color="Olive">b</font>,<font color="Olive">f</font>] &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b</font>,<font color="Olive">c</font>,<font color="Olive">g</font>] holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive">a</font>,<font color="Olive">c</font>,<font color="Olive">g</font> <a href="partfun1.html#K1">*</a> <font color="Olive">f</font>]
 
<b>by </b><i/>;<br/>
<a NAME="E2:19_1"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">a</font> being  <a href="waybel_0.html#NM8">LATTICE</a>  st <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive">a</font>,<font color="Olive">a</font>, <a href="grcat_1.html#K7">id</a> <font color="Olive">a</font>]
 
<b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">C</font> being  <a href="altcat_1.html#V6">strict</a> <a href="altcat_1.html#NM4">category</a><b> such that </b><br/><a NAME="E4:19_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">C</font> is <a href="yellow21.html#V2" target="_self">lattice-wise</a>
 <b>and </b><br/><a NAME="E5:19_1"/><i><font color="Green">E48</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>and </b><br/><a NAME="E6:19_1"/><i><font color="Green">E49</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="waybel_0.html#NM8">LATTICE</a><br/> for <font color="Olive">f</font> being <a href="orders_3.html#V5">monotone</a> <a href="struct_0.html#NM6">Function</a> of <font color="Olive">a</font>,<font color="Olive">b</font> holds <br/> ( <font color="Olive">f</font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C</font> <a href="binop_1.html#K1">.</a> <font color="Olive">a</font>,<font color="Olive">b</font> iff ( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">a</font>,<font color="Olive">b</font>,<font color="Olive">f</font>] ) )
 <b>from </b><i><a class="ref" href="yellow21.html#S1" target="_self">YELLOW21:sch 1</a>(, , );<br/></i>
<b>reconsider </b><font color="Maroon">C</font> = <font color="Maroon">C</font> as  <a href="altcat_1.html#V6">strict</a> <a href="yellow21.html#V2" target="_self">lattice-wise</a> <a href="altcat_1.html#NM4">category</a> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">C</font>
;<br/>

<b>thus </b><a NAME="E8:19_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>by </b><i/>;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font>, <font color="Maroon">b</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font>;<br/>

<b>thus </b><a NAME="E9:19_1"/>
for <font color="Olive">f</font> being <a href="orders_3.html#V5">monotone</a> <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">b</font></span>)</span> holds <br/> ( <font color="Olive">f</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="altcat_1.html#K1">^&gt;</a></span> iff <font color="Maroon">P<sub>1</sub></font>[ <a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">a</font>, <a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">b</font>,<font color="Olive">f</font>] )
 <b>by </b><i>, </i>;<br/>


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