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<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/>



<b>set </b><font color="Maroon">f</font> =  <a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font>;<br/>
<b>set </b><font color="Maroon">g</font> =  <a href="topgrp_1.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span>;<br/>
<a NAME="E1:25"/><i><font color="Green">E30</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font></span>)</span> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> &amp;  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:25_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 ;<br/><b>then reconsider </b><font color="Maroon">y1</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> ;<br/><b>reconsider </b><font color="Maroon">h</font> =  <a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font> as   <a href="funct_1.html#NM1">Function</a> ;<br/><a NAME="E4:25_1"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/><a NAME="E5:25_1"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">y1</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font></span>)</span>
 ;<br/><a NAME="E6:25_1"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><a NAME="E7:25_1"/><b>then </b><i><font color="Green">E47</font></i>: 
( <span class="p1">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font></span>)</span> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font></span>)</span> )
 ;<br/><a NAME="E8:25_1"/><i><font color="Green">E49</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/><span class="p1">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y1</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">y1</font> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">y1</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<font color="Maroon">y1</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D6">GROUP_1:def 6</a></i>
<br/>.= 
<font color="Maroon">y</font>
<b>by </b><i><a class="ref" href="group_1.html#D5">GROUP_1:def 5</a></i>
<br/>.= 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T57">FUNCT_1:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font></span>)</span> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i>, <a class="ref" href="tops_2.html#D4">TOPS_2:def 4</a></i>
;<br/><b>hence </b><a NAME="E10:25_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font></span>)</span> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:25"/>
<span class="p1">(<span class="default"><a href="topgrp_1.html#K2" target="_self">*</a> <font color="Maroon">a</font></span>)</span> <a href="tops_2.html#K2">/"</a>  <a href="funct_2.html#R2">=</a>  <a href="topgrp_1.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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