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

<b>let </b><font color="Maroon">R</font> be   <a href="vectsp_2.html#NM3">Skew-Field</a>;<br/>

<a NAME="E1:22"/><i><font color="Green">E31</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" target="_self">MultGroup</a> <font color="Maroon">R</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E2:22"/>
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">R</font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D21">VECTSP_1:def 21</a></i>;<br/>
<a NAME="E3:22"/><b>then </b>
not  <a href="group_1.html#K2">1.</a> <font color="Maroon">R</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">uR</font> =  <a href="group_1.html#K2">1.</a> <font color="Maroon">R</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" target="_self">MultGroup</a> <font color="Maroon">R</font></span>)</span> <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">h</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" target="_self">MultGroup</a> <font color="Maroon">R</font></span>)</span>;<br/><b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">h</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E2:22_1"/>
<font color="Maroon">g</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">R</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>;<br/><b>hence </b><a NAME="E3:22_1"/>
<font color="Maroon">h</font> <a href="group_1.html#K1">*</a> <font color="Maroon">uR</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font>
 <b>by </b><i/>;<br/><a NAME="E4:22_1"/>
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D19">VECTSP_1:def 19</a></i>;<br/><b>hence </b><a NAME="E5:22_1"/>
<font color="Maroon">uR</font> <a href="group_1.html#K1">*</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:22"/>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <span class="p1">(<span class="default"><a href="uniroots.html#K1" target="_self">MultGroup</a> <font color="Maroon">R</font></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#D5">GROUP_1:def 5</a></i>;<br/>


</div>
