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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:16_2_1_1"/><i><font color="Green" title="E9">A3</font></i>: 
<font color="Maroon" title="c2">F</font> is <a href="group_7.html#V3" title="GROUP_7:attr.3">associative</a>
 ;<br/><b>let </b><font color="Maroon" title="c3">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font>;<br/><a NAME="E2:16_2_1_1"/>
 ex <font color="Olive" title="b1">Fi</font> being non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a>  <a href="group_1.html#L1" title="GROUP_1:struct.1">HGrStr</a>  st <font color="Olive" title="b1">Fi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="group_7.html#K1" title="GROUP_7:func.1">.</a> <font color="Maroon" title="c3">i</font>
 <b>by </b><i><a class="txt" href="group_7.html#E1:16_2_1_1"><i><font color="Green" title="E9">A3</font></i></a>, <a class="ref" href="group_7.html#D4" target="_self" title="GROUP_7:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E3:16_2_1_1"/>
<font color="Maroon" title="c2">F</font> <a href="group_7.html#K1" title="GROUP_7:func.1">.</a> <font color="Maroon" title="c3">i</font> is <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:16_2_1"/><i><font color="Green" title="E9">A4</font></i>: 
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font> holds  <font color="Maroon" title="c2">F</font> <a href="group_7.html#K1" title="GROUP_7:func.1">.</a> <font color="Olive" title="b1">i</font> is <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_7.html#D4" target="_self" title="GROUP_7:def.4">GROUP_7:def 4</a><br/>

<b>assume </b><a NAME="E3:16_2_1"/>
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">i1</font> = <font color="Maroon" title="c3">i</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">Fi</font> = <font color="Maroon" title="c2">F</font> <a href="group_7.html#K1" title="GROUP_7:func.1">.</a> <font color="Maroon" title="c4">i1</font> as  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a>  <a href="group_1.html#L1" title="GROUP_1:struct.1">HGrStr</a>  <b>by </b><i><a class="txt" href="group_7.html#E2:16_2_1"><i><font color="Green" title="E9">A4</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">Fi</font>
;<br/>

<b>thus </b><a NAME="E6:16_2_1"/>
<font color="Maroon" title="c5">Fi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font>
 ;<br/>


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