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<div class="add">

<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="vectsp_2.html#NM3" title="VECTSP_2:NM.3">Skew-Field</a>;<br/>

<a NAME="E1:34"/><i><font color="Green" title="E29">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p2">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="group_2.html#D5" title="GROUP_2:def.5">GROUP_2:def 5</a></i>;<br/>
<a NAME="E2:34"/><i><font color="Green" title="E30">A2</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="uniroots.html#D1" title="UNIROOTS:def.1">UNIROOTS:def 1</a></i>;<br/>
<a NAME="E3:34"/><i><font color="Green" title="E31">A3</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="ref" href="uniroots.html#T18" title="UNIROOTS:th.18">UNIROOTS:18</a></i>;<br/>
<a NAME="E4:34"/><i><font color="Green" title="E32">A4</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="ref" href="weddwitt.html#T17" target="_self" title="WEDDWITT:th.17">Th17</a></i>;<br/>
<a NAME="E5:34"/><i><font color="Green" title="E33">A5</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p2">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">x</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="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:34_1"/><i><font color="Green" title="E34">A6</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p2">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:34_1_1"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p2">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 </span><b>by </b><i><a class="txt" href="weddwitt.html#E1:34_1"><i><font color="Green" title="E34">A6</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_1_1"><b>suppose </b></a><a NAME="E1:34_1_1_1"/><i><font color="Green" title="E35">A7</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p2">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c3">a</font> = <font color="Maroon" title="c2">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span> <b>by </b><i><a class="txt" href="weddwitt.html#E1:34"><i><font color="Green" title="E29">A1</font></i></a></i>;<br/><a NAME="E3:34_1_1_1"/><i><font color="Green" title="E36">A8</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a>  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span>
 <b>by </b><i><a class="txt" href="weddwitt.html#E1:34_1_1_1"><i><font color="Green" title="E35">A7</font></i></a>, <a class="ref" href="rlvect_1.html#D1" title="RLVECT_1:def.1">RLVECT_1:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c4">a1</font> = <font color="Maroon" title="c3">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="ref" href="uniroots.html#T22" title="UNIROOTS:th.22">UNIROOTS:22</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>;<br/><b>thus </b><a NAME="E1:34_1_1_1_1"/>
<font color="Maroon" title="c4">a1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c4">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_1_1_1_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:34_1_1_1_1_1_1"/>
( <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span> or <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 </span><b>by </b><i><a class="txt" href="weddwitt.html#E3:34"><i><font color="Green" title="E31">A3</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:34_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c6">b1</font> = <font color="Maroon" title="c5">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span> ;<br/><b>thus </b><font color="Maroon" title="c4">a1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c5">b</font> = 
<font color="Maroon" title="c3">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c6">b1</font>
<b>by </b><i><a class="ref" href="uniroots.html#T19" title="UNIROOTS:th.19">UNIROOTS:19</a></i>
<br/>.= 
<font color="Maroon" title="c6">b1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c3">a</font>
<b>by </b><i><a class="txt" href="weddwitt.html#E3:34_1_1_1"><i><font color="Green" title="E36">A8</font></i></a>, <a class="ref" href="group_5.html#T89" title="GROUP_5:th.89">GROUP_5:89</a></i>
<br/>.= 
<font color="Maroon" title="c5">b</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c4">a1</font>
<b>by </b><i><a class="ref" href="uniroots.html#T19" title="UNIROOTS:th.19">UNIROOTS:19</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:34_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:34_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green" title="E37">A9</font></i>: 
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><font color="Maroon" title="c4">a1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c5">b</font> = 
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#T36" title="VECTSP_1:th.36">VECTSP_1:36</a></i>
<br/>.= 
<font color="Maroon" title="c5">b</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c4">a1</font>
<b>by </b><i><a class="txt" href="weddwitt.html#E2:34_1_1_1_1_1_1_2"><i><font color="Green" title="E37">A9</font></i></a>, <a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div></div><b>end;</b></div><a NAME="E6:34_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">a1</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a>  <a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="ref" href="weddwitt.html#T18" target="_self" title="WEDDWITT:th.18">Th18</a></i>;<br/><b>hence </b><a NAME="E7:34_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D1" title="RLVECT_1:def.1">RLVECT_1:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_1_2"><b>suppose </b></a><a NAME="E1:34_1_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:34_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:34_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a>  <a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="ref" href="weddwitt.html#T19" target="_self" title="WEDDWITT:th.19">Th19</a></i>;<br/><b>hence </b><a NAME="E4:34_1_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D1" title="RLVECT_1:def.1">RLVECT_1:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E6:34"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p2">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">x</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="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:34_2"/><i><font color="Green" title="E34">A10</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c3">a</font> = <font color="Maroon" title="c2">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c4">a1</font> = <font color="Maroon" title="c3">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="txt" href="weddwitt.html#E4:34"><i><font color="Green" title="E32">A4</font></i></a>, <a class="txt" href="weddwitt.html#E1:34_2"><i><font color="Green" title="E34">A10</font></i></a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:34_2_1"/>
( <font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font> or <font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_2_1_1"><b>suppose </b></a><a NAME="E1:34_2_1_1"/>
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font>
 ;<br/><div class="add"><a NAME="E2:34_2_1_1"/><b>then </b>
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:34_2_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p2">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_2_1_2"><b>suppose </b></a><a NAME="E1:34_2_1_2"/>
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font>
 ;<br/><div class="add"><a NAME="E2:34_2_1_2"/><b>then </b>
not <font color="Maroon" title="c4">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c5">a2</font> = <font color="Maroon" title="c4">a1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span> <b>by </b><i><a class="txt" href="weddwitt.html#E2:34"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_2_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span>;<br/><a NAME="E1:34_2_1_2_1"/><i><font color="Green" title="E35">A11</font></i>: 
<font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span>
 ;<br/><a NAME="E2:34_2_1_2_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="txt" href="weddwitt.html#E2:34"><i><font color="Green" title="E30">A2</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c7">b1</font> = <font color="Maroon" title="c6">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="txt" href="weddwitt.html#E1:34_2_1_2_1"><i><font color="Green" title="E35">A11</font></i></a></i>;<br/><a NAME="E4:34_2_1_2_1"/><i><font color="Green" title="E36">A12</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a>  <a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="txt" href="weddwitt.html#E1:34_2"><i><font color="Green" title="E34">A10</font></i></a>, <a class="ref" href="rlvect_1.html#D1" title="RLVECT_1:def.1">RLVECT_1:def 1</a></i>;<br/><b>thus </b><font color="Maroon" title="c5">a2</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c6">b</font> = 
<font color="Maroon" title="c4">a1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c7">b1</font>
<b>by </b><i><a class="ref" href="uniroots.html#T19" title="UNIROOTS:th.19">UNIROOTS:19</a></i>
<br/>.= 
<font color="Maroon" title="c7">b1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c4">a1</font>
<b>by </b><i><a class="txt" href="weddwitt.html#E4:34_2_1_2_1"><i><font color="Green" title="E36">A12</font></i></a>, <a class="ref" href="weddwitt.html#T18" target="_self" title="WEDDWITT:th.18">Th18</a></i>
<br/>.= 
<font color="Maroon" title="c6">b</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c5">a2</font>
<b>by </b><i><a class="ref" href="uniroots.html#T19" title="UNIROOTS:th.19">UNIROOTS:19</a></i>
;<br/></div><b>end;</b></div><a NAME="E5:34_2_1_2"/><b>then </b>
<font color="Maroon" title="c4">a1</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a>  <a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span>
 <b>by </b><i><a class="ref" href="group_5.html#T89" title="GROUP_5:th.89">GROUP_5:89</a></i>;<br/><a NAME="E6:34_2_1_2"/><b>then </b>
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p2">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D1" title="RLVECT_1:def.1">RLVECT_1:def 1</a></i>;<br/><b>hence </b><a NAME="E7:34_2_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p2">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E7:34"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_5.html#K10" title="GROUP_5:func.10">center</a> <span class="p2">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="weddwitt.html#E5:34"><i><font color="Green" title="E33">A5</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>


</div>
