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<b>let </b><font color="Maroon" title="c1">UN</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>;<br/>

<b>reconsider </b><font color="Maroon" title="c2">u</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font> <b>by </b><i><a class="ref" href="classes2.html#T62" title="CLASSES2:th.62">CLASSES2:62</a></i>;<br/>
<b>set </b><font color="Maroon" title="c3">x1</font> = <span class="p1"><a href="classes2.html#K1" title="CLASSES2:func.1">{</a><span class="default"><font color="Maroon" title="c2">u</font></span><a href="classes2.html#K1" title="CLASSES2:func.1">}</a></span>;<br/>
<a NAME="E2:75"/>
 <a href="algstr_1.html#K1" title="ALGSTR_1:func.1">Extract</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">u</font>
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">x4</font> =  <a href="algstr_1.html#K1" title="ALGSTR_1:func.1">Extract</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">x3</font> =  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">comp</a> <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font> <b>by </b><i><a class="ref" href="grcat_1.html#T6" target="_self" title="GRCAT_1:th.6">Th6</a>, <a class="ref" href="grcat_1.html#T13" target="_self" title="GRCAT_1:th.13">Th13</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">x2</font> =  <a href="funct_5.html#K9" title="FUNCT_5:func.9">op2</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font> <b>by </b><i><a class="ref" href="grcat_1.html#T6" target="_self" title="GRCAT_1:th.6">Th6</a></i>;<br/>
<b>take </b><font color="Maroon" title="c7">x</font> = <span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><span class="p2"><a href="classes2.html#K1" title="CLASSES2:func.1">{</a><span class="default"><font color="Maroon" title="c2">u</font></span><a href="classes2.html#K1" title="CLASSES2:func.1">}</a></span>,<font color="Maroon" title="c6">x2</font>,<font color="Maroon" title="c5">x3</font>,<font color="Maroon" title="c4">x4</font></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span>;<br/>

<b>thus </b><a NAME="E6:75"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">UN</font>
 <b>by </b><i><a class="ref" href="grcat_1.html#T3" target="_self" title="GRCAT_1:th.3">Th3</a></i>;<br/>

<b>take </b>
<span class="p1"><a href="classes2.html#K1" title="CLASSES2:func.1">{</a><span class="default"><font color="Maroon" title="c2">u</font></span><a href="classes2.html#K1" title="CLASSES2:func.1">}</a></span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="grcat_1.html#D28" target="_self" title="GRCAT_1:def.28">GRCAT_1:def 28</a><br/>

<b>take </b>
<font color="Maroon" title="c6">x2</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c5">x3</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c4">x4</font>
;<br/>

<b>thus </b><a NAME="E7:75"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><span class="p2"><a href="classes2.html#K1" title="CLASSES2:func.1">{</a><span class="default"><font color="Maroon" title="c2">u</font></span><a href="classes2.html#K1" title="CLASSES2:func.1">}</a></span>,<font color="Maroon" title="c6">x2</font>,<font color="Maroon" title="c5">x3</font>,<font color="Maroon" title="c4">x4</font></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span>
 ;<br/>

<b>take </b>
 <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a> 
;<br/>

<b>thus </b><a NAME="E8:75"/>
(  <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a>  &amp; <span class="p1"><a href="classes2.html#K1" title="CLASSES2:func.1">{</a><span class="default"><font color="Maroon" title="c2">u</font></span><a href="classes2.html#K1" title="CLASSES2:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a>  &amp; <font color="Maroon" title="c6">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a>  &amp; <font color="Maroon" title="c5">x3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">comp</a> <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a>  &amp; <font color="Maroon" title="c4">x4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a>  )
 <b>by </b><i><a class="ref" href="card_1.html#T87" title="CARD_1:th.87">CARD_1:87</a></i>;<br/>


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