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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="setfam_1.html#V2">with_non-empty_element</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="waybel_0.html#NM8">LATTICE</a>;<br/>



<b>assume </b><a NAME="E1:65"/><i><font color="Green">E27</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:65_1"/>
<font color="Maroon">c<sub>2</sub></font> is   <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="yellow21.html#K8" target="_self">-ALG_category</a> </span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <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="yellow21.html#K8" target="_self">-ALG_category</a> </span>)</span> ;<br/><a NAME="E3:65_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow21.html#K4" target="_self">latt</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> is   <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="yellow21.html#K7" target="_self">-CONT_category</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="altcat_2.html#T30">ALTCAT_2:30</a></i>;<br/><b>hence </b><a NAME="E4:65_1"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="orders_2.html#V1">strict</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="lattice3.html#V3">complete</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="waybel_8.html#V2">algebraic</a> )
 <b>by </b><i><a class="txt" href="yellow21.html#E1:65"><i><font color="Green">E27</font></i></a>, <a class="ref" href="yellow21.html#D12" target="_self">Def12</a>, <a class="ref" href="yellow21.html#T17" target="_self">Th17</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:65"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="orders_2.html#V1">strict</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="lattice3.html#V3">complete</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="waybel_8.html#V2">algebraic</a> )
 ;<br/>

<a NAME="E4:65"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is  <a href="orders_2.html#V1">strict</a> <a href="lattice3.html#V3">complete</a> <a href="waybel_8.html#V2">algebraic</a> <a href="waybel_0.html#NM8">LATTICE</a>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <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="yellow21.html#K7" target="_self">-CONT_category</a> </span>)</span> <b>by </b><i><a class="txt" href="yellow21.html#E1:65"><i><font color="Green">E27</font></i></a>, <a class="ref" href="yellow21.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E6:65"/>
 <a href="yellow21.html#K4" target="_self">latt</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
;<br/>
<b>hence </b><a NAME="E7:65"/>
<font color="Maroon">c<sub>2</sub></font> is   <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="yellow21.html#K8" target="_self">-ALG_category</a> </span>)</span>
 <b>by </b><i><a class="txt" href="yellow21.html#E3:65"><i><font color="Green">E28</font></i></a>, <a class="ref" href="yellow21.html#D12" target="_self">Def12</a></i>;<br/>


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