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

<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="ring_1.html#K1" target="_self">EqRel</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></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">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:33_1_1_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:33_1_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>6</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>6</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E2:33_1_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="ring_1.html#E4:33_1_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="ring_1.html#T13" target="_self">Th13</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="ring_1.html#E2:33_1_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="ring_1.html#E4:33_1_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="ring_1.html#T13" target="_self">Th13</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#D6">RLVECT_1:def 6</a>
<div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:33_1_1_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:33_1_1_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>6</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:33_1_1_2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E8:33_1_1_2"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>6</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E10:33_1_1_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E11:33_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>6</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ring_1.html#E2:33_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="ring_1.html#E4:33_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="ring_1.html#T13" target="_self">Th13</a></i>;<br/><a NAME="E12:33_1_1_2"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="ring_1.html#E8:33_1_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E13:33_1_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ring_1.html#E4:33_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="ring_1.html#E6:33_1_1_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="ring_1.html#T13" target="_self">Th13</a></i>;<br/><a NAME="E14:33_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="ring_1.html#E10:33_1_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E15:33_1_1_2"/><b>then </b><i><font color="Green">E28</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="ring_1.html#E12:33_1_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="ideal_1.html#T15">IDEAL_1:15</a></i>;<br/><i><font color="Green">E29</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></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">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></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">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></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">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></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">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="ref" href="ring_1.html#T1" target="_self">Th1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></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">c<sub>11</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>12</sub></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">c<sub>5</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E6:33_1_1_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="ring_1.html#E8:33_1_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="ring_1.html#T13" target="_self">Th13</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E16:33_1_1_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="ring_1.html#E15:33_1_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E2:33_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="ring_1.html#E10:33_1_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="ring_1.html#T13" target="_self">Th13</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#D7">RLVECT_1:def 7</a>
<div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:33_1_1_3"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font> )
 <b>and </b><br/><a NAME="E3:33_1_1_3"/><i><font color="Green">E23</font></i>: 
the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="ring_1.html#D6" target="_self">Def6</a></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">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="ring_1.html#D6" target="_self">Def6</a></i>;<br/><a NAME="E5:33_1_1_3"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="ring_1.html#E2:33_1_1_3"><i><font color="Green">E22</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E6:33_1_1_3"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T26">RLVECT_1:26</a></i>;<br/><i><font color="Green">E26</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T28">RLVECT_1:28</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></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">c<sub>5</sub></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">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></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">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="ring_1.html#E2:33_1_1_3"><i><font color="Green">E22</font></i></a>, <a class="txt" href="ring_1.html#E3:33_1_1_3"><i><font color="Green">E23</font></i></a>, <a class="txt" href="ring_1.html#E7:33_1_1_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="ring_1.html#E6:33_1_1_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="ring_1.html#E5:33_1_1_3"><i><font color="Green">E24</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</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">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:33_1_1_4"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="ring_1.html#D6" target="_self">Def6</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>8</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="ref" href="ring_1.html#T12" target="_self">Th12</a></i>;<br/><b>take </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font>;<br/><a NAME="E5:33_1_1_4"/><i><font color="Green">E23</font></i>: 
 <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="ring_1.html#D6" target="_self">Def6</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>9</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E2:33_1_1_4"><i><font color="Green">E22</font></i></a>, <a class="ref" href="ring_1.html#T13" target="_self">Th13</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E5:33_1_1_4"><i><font color="Green">E23</font></i></a>, <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">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:33_1_1_5"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:33_1_1_5"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>6</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:33_1_1_5"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E8:33_1_1_5"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E10:33_1_1_5"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E11:33_1_1_5"/>
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ring_1.html#E2:33_1_1_5"><i><font color="Green">E22</font></i></a>, <a class="txt" href="ring_1.html#E4:33_1_1_5"><i><font color="Green">E23</font></i></a>, <a class="ref" href="ring_1.html#T14" target="_self">Th14</a></i>;<br/><a NAME="E12:33_1_1_5"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="ring_1.html#E8:33_1_1_5"><i><font color="Green">E25</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E13:33_1_1_5"/><b>then </b><i><font color="Green">E27</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></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">c<sub>6</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ring_1.html#E4:33_1_1_5"><i><font color="Green">E23</font></i></a>, <a class="txt" href="ring_1.html#E6:33_1_1_5"><i><font color="Green">E24</font></i></a>, <a class="ref" href="ring_1.html#T14" target="_self">Th14</a></i>;<br/><a NAME="E15:33_1_1_5"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="ring_1.html#E10:33_1_1_5"><i><font color="Green">E26</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E16:33_1_1_5"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></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">E29</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></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">E30</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></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">E31</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></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">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>12</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="ring_1.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E21:33_1_1_5"/><b>then </b><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="ring_1.html#E13:33_1_1_5"><i><font color="Green">E27</font></i></a>, <a class="txt" href="ring_1.html#E16:33_1_1_5"><i><font color="Green">E28</font></i></a>, <a class="txt" href="ring_1.html#E17:33_1_1_5"><i><font color="Green">E29</font></i></a>, <a class="txt" href="ring_1.html#E18:33_1_1_5"><i><font color="Green">E30</font></i></a>, <a class="txt" href="ring_1.html#E19:33_1_1_5"><i><font color="Green">E31</font></i></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">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E6:33_1_1_5"><i><font color="Green">E24</font></i></a>, <a class="txt" href="ring_1.html#E8:33_1_1_5"><i><font color="Green">E25</font></i></a>, <a class="ref" href="ring_1.html#T14" target="_self">Th14</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E21:33_1_1_5"><i><font color="Green">E32</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E2:33_1_1_5"><i><font color="Green">E22</font></i></a>, <a class="txt" href="ring_1.html#E10:33_1_1_5"><i><font color="Green">E26</font></i></a>, <a class="ref" href="ring_1.html#T14" target="_self">Th14</a></i>
;<br/></div>
<b>end;</b></div>

<a NAME="E6:33_1_1"/><i><font color="Green">E22</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="ring_1.html#T15" target="_self">Th15</a></i>;<br/>
<b>hence </b><a NAME="E7:33_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="ring_1.html#E22"><i><font color="Green">Lemma19</font></i></a></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">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> holds <font color="Olive">b<sub>1</sub></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">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="ring_1.html#E6:33_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="ring_1.html#E22"><i><font color="Green">Lemma19</font></i></a></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">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">c<sub>2</sub></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">c<sub>8</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E10:33_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E12:33_1_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>6</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E14:33_1_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E16:33_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E18:33_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E20:33_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E21:33_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="ring_1.html#E12:33_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="ring_1.html#E14:33_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="ring_1.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E22:33_1_1"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="ring_1.html#E16:33_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E23:33_1_1"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></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">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="ring_1.html#E10:33_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="ring_1.html#E12:33_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="ring_1.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E25:33_1_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="ring_1.html#E18:33_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E26:33_1_1"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="ring_1.html#E23:33_1_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="ideal_1.html#T15">IDEAL_1:15</a></i>;<br/>
<a NAME="E27:33_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="ring_1.html#E10:33_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="ring_1.html#E14:33_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="ring_1.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E28:33_1_1"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="ring_1.html#E20:33_1_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E29:33_1_1"/><b>then </b><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="ring_1.html#E26:33_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="ideal_1.html#T15">IDEAL_1:15</a></i>;<br/>
<i><font color="Green">E33</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>11</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ring_1.html#T1" target="_self">Th1</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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>13</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>13</sub></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">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="ref" href="ring_1.html#T1" target="_self">Th1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>13</sub></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">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E10:33_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="ring_1.html#E16:33_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="ring_1.html#T14" target="_self">Th14</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>13</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E30:33_1_1"><i><font color="Green">E33</font></i></a>, <a class="txt" href="ring_1.html#E29:33_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E18:33_1_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="ring_1.html#E20:33_1_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="ring_1.html#T13" target="_self">Th13</a></i>
;<br/>

<b>consider </b><font color="Maroon">c<sub>14</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E33:33_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>15</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E35:33_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="ref" href="ring_1.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E36:33_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="ring_1.html#E10:33_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="ring_1.html#E12:33_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="ring_1.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E37:33_1_1"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="ring_1.html#E33:33_1_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E38:33_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="ring_1.html#E10:33_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="ring_1.html#E14:33_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="ring_1.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E39:33_1_1"/><b>then </b><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="ring_1.html#E35:33_1_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E40:33_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="ring_1.html#E22:33_1_1"><i><font color="Green">E29</font></i></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">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></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<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="ring_1.html#E37:33_1_1"><i><font color="Green">E36</font></i></a>, <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">E38</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></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">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>14</sub></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<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="ring_1.html#E39:33_1_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="ideal_1.html#D1">IDEAL_1:def 1</a></i>;<br/>
<i><font color="Green">E39</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></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">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>14</sub></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<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></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">c<sub>9</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></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">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>14</sub></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<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>15</sub></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">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></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">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></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">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>14</sub></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<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>15</sub></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">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></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">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>14</sub></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<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>15</sub></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">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>14</sub></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<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>15</sub></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">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>15</sub></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">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>15</sub></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">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="ref" href="ring_1.html#T1" target="_self">Th1</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">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>15</sub></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">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="ref" href="ring_1.html#T1" target="_self">Th1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>15</sub></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">c<sub>6</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E16:33_1_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="ring_1.html#E10:33_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="ring_1.html#T14" target="_self">Th14</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E43:33_1_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="ring_1.html#E42:33_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="ring_1.html#T6" target="_self">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ring_1.html#E33:33_1_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="ring_1.html#E35:33_1_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="ring_1.html#T13" target="_self">Th13</a></i>
;<br/>


</div>
