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<b>let </b><font color="Maroon">L1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/>

<b>take </b>
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">L1</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="quofield.html#D26">QUOFIELD:def 26</a><br/>

<b>thus </b><a NAME="E1:2_1_1"/>
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">L1</font> is <a href="quofield.html#V1">RingHomomorphism</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="quofield.html#D23">QUOFIELD:def 23</a>,<a class="ref" href="quofield.html#D24">QUOFIELD:def 24</a><br/>

<b>thus </b><a NAME="E2:2_1_1"/>
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">L1</font> is <a href="funct_1.html#V2">one-to-one</a>
 ;<br/>

<b>thus </b><a NAME="E3:2_1_1"/>
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">L1</font> is <a href="quofield.html#V1">RingHomomorphism</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="quofield.html#D22">QUOFIELD:def 22</a><br/>

<b>thus </b> <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">L1</font></span>)</span> = 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">L1</font>
<b>by </b><i><a class="ref" href="topgrp_1.html#T1">TOPGRP_1:1</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font>
<b>by </b><i><a class="ref" href="pre_topc.html#T12">PRE_TOPC:12</a></i>
;<br/>


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