<?xml version="1.0"?>
<div class="add">

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:16_3_1_1"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">F</font> is <a href="group_7.html#V4" target="_self">commutative</a>
 ;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font>;<br/><a NAME="E2:16_3_1_1"/>
 ex <font color="Olive">Fi</font> being non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V7">commutative</a>  <a href="group_1.html#L1">HGrStr</a>  st <font color="Olive">Fi</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="group_7.html#K1" target="_self">.</a> <font color="Maroon">i</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:16_3_1_1"/>
<font color="Maroon">F</font> <a href="group_7.html#K1" target="_self">.</a> <font color="Maroon">i</font> is <a href="group_1.html#V7">commutative</a>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:16_3_1"/><i><font color="Green">E55</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font> holds  <font color="Maroon">F</font> <a href="group_7.html#K1" target="_self">.</a> <font color="Olive">i</font> is <a href="group_1.html#V7">commutative</a>
 ;<br/>

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_7.html#D5" target="_self">GROUP_7:def 5</a><br/>

<b>assume </b><a NAME="E3:16_3_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">i1</font> = <font color="Maroon">i</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font> ;<br/>
<b>reconsider </b><font color="Maroon">Fi</font> = <font color="Maroon">F</font> <a href="group_7.html#K1" target="_self">.</a> <font color="Maroon">i1</font> as  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V7">commutative</a>  <a href="group_1.html#L1">HGrStr</a>  <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">Fi</font>
;<br/>

<b>thus </b><a NAME="E6:16_3_1"/>
<font color="Maroon">Fi</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/>


</div>
