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

<b>set </b><font color="Maroon">E</font> =  <a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font>;<br/>
<b>set </b><font color="Maroon">g</font> = the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D5">RLVECT_1:def 5</a>
<div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>;<br/><b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E2:33_1_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">a</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E4:33_1_1_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">b</font>
 <b>by </b><i/>;<br/><b>thus </b><font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">y</font> = 
 <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">x</font>
<b>by </b><i>, , </i>
;<br/></div>
<b>end;</b></div>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a>
<div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>, <font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>;<br/><b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E2:33_1_1_2"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">a</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E4:33_1_1_2"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">b</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">c</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E6:33_1_1_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">c</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">ab</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E8:33_1_1_2"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">ab</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">bc</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E10:33_1_1_2"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">bc</font>
 <b>by </b><i/>;<br/><a NAME="E11:33_1_1_2"/>
<font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i>, , </i>;<br/><a NAME="E12:33_1_1_2"/><b>then </b><i><font color="Green">E65</font></i>: 
<font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="ring_1.html#T1" target="_self">Th1</a>, </i>;<br/><a NAME="E13:33_1_1_2"/>
<font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span>
 <b>by </b><i>, , </i>;<br/><a NAME="E14:33_1_1_2"/><b>then </b>
<font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i>, </i>;<br/><a NAME="E15:33_1_1_2"/><b>then </b><i><font color="Green">E68</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i>, <a class="ref" href="ideal_1.html#T15">IDEAL_1:15</a></i>;<br/><i><font color="Green">E69</font></i>: <span class="p1">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T43">RLVECT_1:43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">bc</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T42">RLVECT_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">bc</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T41">RLVECT_1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">bc</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">bc</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">bc</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T42">RLVECT_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">bc</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T41">RLVECT_1:41</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">y</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font> = 
 <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ring_1.html#T1" target="_self">Th1</a>, </i>
<br/>.= 
 <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">bc</font></span>)</span>
<b>by </b><i><a class="ref" href="ring_1.html#T2" target="_self">Th2</a>, , </i>
<br/>.= 
<font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i>, , </i>
;<br/></div>
<b>end;</b></div>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a>
<div class="add"><b>let </b><font color="Maroon">v</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>;<br/><b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>, <font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E2:33_1_1_3"/><i><font color="Green">E70</font></i>: 
( <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">a</font> &amp;  <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">b</font> )
 <b>and </b><br/><a NAME="E3:33_1_1_3"/><i><font color="Green">E72</font></i>: 
the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">v</font>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E4:33_1_1_3"/>
 <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E5:33_1_1_3"/><b>then </b><i><font color="Green">E77</font></i>: 
<font color="Maroon">b</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i>, </i>;<br/><a NAME="E6:33_1_1_3"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">b</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T26">RLVECT_1:26</a></i>;<br/><i><font color="Green">E79</font></i>: <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T42">RLVECT_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T28">RLVECT_1:28</a></i>
<br/>.= 
<font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a></i>
;<br/><b>thus </b><font color="Maroon">v</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span></span>)</span> = 
the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">v</font>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binop_1.html#D1">BINOP_1:def 1</a></i>
<br/>.= 
<font color="Maroon">v</font>
<b>by </b><i>, , , <a class="ref" href="ring_1.html#T1" target="_self">Th1</a>, , </i>
;<br/></div>
<b>end;</b></div>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D8">RLVECT_1:def 8</a>
<div class="add"><b>let </b><font color="Maroon">v</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>;<br/><b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>, <font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E2:33_1_1_4"/><i><font color="Green">E80</font></i>: 
( <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">a</font> &amp;  <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">b</font> )
 <b>and </b><br/><a NAME="E3:33_1_1_4"/>
the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">v</font>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">w</font> =  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">a</font></span>)</span> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span> <b>by </b><i/>;<br/><b>take </b><font color="Maroon">w</font> = <font color="Maroon">w</font>;<br/><a NAME="E5:33_1_1_4"/><i><font color="Green">E81</font></i>: 
 <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font></span>)</span>
 <b>by </b><i/>;<br/><b>thus </b><font color="Maroon">v</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">w</font> = 
 <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i>, <a class="ref" href="rlvect_1.html#D10">RLVECT_1:def 10</a></i>
;<br/></div>
<b>end;</b></div>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a>
<div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>, <font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>;<br/><b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E2:33_1_1_5"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">a</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E4:33_1_1_5"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">b</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">c</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E6:33_1_1_5"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">c</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">ab</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E8:33_1_1_5"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">ab</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">bc</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E10:33_1_1_5"/><i><font color="Green">E86</font></i>: 
<font color="Maroon">y</font> <a href="group_1.html#K1">*</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">bc</font>
 <b>by </b><i/>;<br/><a NAME="E11:33_1_1_5"/>
<font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i>, , </i>;<br/><a NAME="E12:33_1_1_5"/><b>then </b>
<font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="ring_1.html#T1" target="_self">Th1</a>, </i>;<br/><a NAME="E13:33_1_1_5"/><b>then </b><i><font color="Green">E87</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="ideal_1.html#D3">IDEAL_1:def 3</a></i>;<br/><a NAME="E14:33_1_1_5"/>
<font color="Maroon">y</font> <a href="group_1.html#K1">*</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span>
 <b>by </b><i>, , </i>;<br/><a NAME="E15:33_1_1_5"/><b>then </b>
<font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i>, </i>;<br/><a NAME="E16:33_1_1_5"/><b>then </b><i><font color="Green">E88</font></i>: 
<font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="ideal_1.html#D2">IDEAL_1:def 2</a></i>;<br/><a NAME="E17:33_1_1_5"/><i><font color="Green">E91</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">ab</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T45">VECTSP_1:45</a></i>;<br/><a NAME="E18:33_1_1_5"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T43">VECTSP_1:43</a></i>;<br/><a NAME="E19:33_1_1_5"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/><a NAME="E20:33_1_1_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">ab</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">ab</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E21:33_1_1_5"/><b>then </b><i><font color="Green">E94</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">ab</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i>, , <a class="ref" href="ring_1.html#T2" target="_self">Th2</a>, , <a class="ref" href="ring_1.html#T3" target="_self">Th3</a>, <a class="ref" href="ideal_1.html#T15">IDEAL_1:15</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">y</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">z</font> = 
 <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">ab</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ring_1.html#T1" target="_self">Th1</a>, </i>
<br/>.= 
 <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="group_1.html#K1">*</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i>, , </i>
;<br/></div>
<b>end;</b></div>

<a NAME="E6:33_1_1"/><i><font color="Green">E95</font></i>: 
 <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<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>  <a href="group_1.html#K2">1.</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:33_1_1"/>
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span> holds  <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">x</font>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_1.html#D19">VECTSP_1:def 19</a><br/>

<b>thus </b><a NAME="E8:33_1_1"/>
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span> holds  <font color="Olive">x</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">x</font>
 <b>by </b><i>, </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a><br/>

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>, <font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_1.html#D18">VECTSP_1:def 18</a><br/>

<b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E10:33_1_1"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">a</font>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E12:33_1_1"/><i><font color="Green">E97</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">b</font>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">c</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E14:33_1_1"/><i><font color="Green">E98</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">c</font>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">bc</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E16:33_1_1"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">bc</font>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">ab</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E18:33_1_1"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">ab</font>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">ac</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E20:33_1_1"/><i><font color="Green">E113</font></i>: 
<font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">ac</font>
 <b>by </b><i/>;<br/>
<a NAME="E21:33_1_1"/>
<font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="ring_1.html#T1" target="_self">Th1</a>, </i>;<br/>
<a NAME="E22:33_1_1"/><b>then </b><i><font color="Green">E114</font></i>: 
<font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E23:33_1_1"/><b>then </b><i><font color="Green">E115</font></i>: 
<font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="ideal_1.html#D2">IDEAL_1:def 2</a></i>;<br/>
<a NAME="E24:33_1_1"/>
<font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E25:33_1_1"/><b>then </b>
<font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E26:33_1_1"/><b>then </b><i><font color="Green">E116</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 
<b>by </b><i>, <a class="ref" href="ideal_1.html#T15">IDEAL_1:15</a></i>;<br/>
<a NAME="E27:33_1_1"/>
<font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="ring_1.html#T1" target="_self">Th1</a>, </i>;<br/>
<a NAME="E28:33_1_1"/><b>then </b>
<font color="Maroon">ac</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E29:33_1_1"/><b>then </b><i><font color="Green">E117</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">ac</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="ring_1.html#T3" target="_self">Th3</a>, <a class="ref" href="ideal_1.html#T15">IDEAL_1:15</a></i>;<br/>
<i><font color="Green">E118</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">ac</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">ac</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T43">VECTSP_1:43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">ac</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D11">VECTSP_1:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">ac</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T41">RLVECT_1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ab</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">ac</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T43">RLVECT_1:43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ab</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ac</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T43">RLVECT_1:43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ab</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ac</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T42">RLVECT_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ab</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ac</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T42">RLVECT_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ab</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ac</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ab</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ac</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T42">RLVECT_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ab</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ac</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T42">RLVECT_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ab</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ac</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">ac</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T41">RLVECT_1:41</a></i>
;<br/>
<b>thus </b><font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font></span>)</span> = 
 <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">bc</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
 <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">ab</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">ac</font></span>)</span>
<b>by </b><i><a class="ref" href="ring_1.html#D1" target="_self">Def1</a>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">y</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i>, , </i>
;<br/>

<b>consider </b><font color="Maroon">ba</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E33:33_1_1"/><i><font color="Green">E120</font></i>: 
<font color="Maroon">y</font> <a href="group_1.html#K1">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">ba</font>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">ca</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E35:33_1_1"/><i><font color="Green">E122</font></i>: 
<font color="Maroon">z</font> <a href="group_1.html#K1">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">ca</font>
 <b>by </b><i/>;<br/>
<a NAME="E36:33_1_1"/>
<font color="Maroon">y</font> <a href="group_1.html#K1">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E37:33_1_1"/><b>then </b><i><font color="Green">E123</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ba</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="ring_1.html#D2" target="_self">Def2</a>, </i>;<br/>
<a NAME="E38:33_1_1"/>
<font color="Maroon">z</font> <a href="group_1.html#K1">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="ring_1.html#T1" target="_self">Th1</a>, </i>;<br/>
<a NAME="E39:33_1_1"/><b>then </b><i><font color="Green">E124</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ca</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E40:33_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="ring_1.html#T2" target="_self">Th2</a>, <a class="ref" href="ideal_1.html#D3">IDEAL_1:def 3</a></i>;<br/>
<a NAME="E41:33_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ba</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 
<b>by </b><i>, <a class="ref" href="ideal_1.html#D1">IDEAL_1:def 1</a></i>;<br/>
<a NAME="E42:33_1_1"/><b>then </b><i><font color="Green">E125</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ba</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ca</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="ring_1.html#D3" target="_self">Def3</a>, <a class="ref" href="ideal_1.html#D1">IDEAL_1:def 1</a></i>;<br/>
<i><font color="Green">E126</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">bc</font> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ba</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ca</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">bc</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ba</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ca</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T45">VECTSP_1:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">bc</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ba</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ca</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D12">VECTSP_1:def 12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">bc</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ba</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ca</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T41">RLVECT_1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">bc</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ba</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ca</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T42">RLVECT_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">bc</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ba</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ca</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T42">RLVECT_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">bc</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ba</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ca</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T42">RLVECT_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">bc</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ba</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ca</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">bc</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ba</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ca</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T42">RLVECT_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">bc</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ba</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">ca</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">bc</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">ba</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">ca</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T41">RLVECT_1:41</a></i>
;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">z</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">x</font> = 
 <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">bc</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
 <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">R</font>,<font color="Maroon">I</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">ba</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">ca</font></span>)</span>
<b>by </b><i><a class="ref" href="ring_1.html#D4" target="_self">Def4</a>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="group_1.html#K1">*</a> <font color="Maroon">x</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="group_1.html#K1">*</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="ring_1.html#D2" target="_self">Def2</a>, , </i>
;<br/>


</div>
