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

<b>let </b><font color="Maroon" title="c1">SF</font> be   <a href="vectsp_2.html#NM3" title="VECTSP_2:NM.3">Skew-Field</a>;<br/><b>let </b><font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">x</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Scalar</a> of <font color="Maroon" title="c1">SF</font>;<br/>





<b>assume </b><a NAME="E1:38"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">SF</font>
 ;<br/>

<b>thus </b><a NAME="E2:38"/><i><font color="Green" title="E22">A2</font></i>: 
 <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">y</font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T41" title="VECTSP_1:th.41">VECTSP_1:41</a></i>;<br/>

<a NAME="E3:38"/><i><font color="Green" title="E23">A3</font></i>: 
 <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">SF</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1"><b>proof </b></a><div class="add">

<a NAME="E1:38_1"/>
 <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">SF</font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D21" title="VECTSP_1:def.21">VECTSP_1:def 21</a></i>;<br/>
<b>hence </b><a NAME="E2:38_1"/>
 <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">SF</font>
 <b>by </b><i><a class="ref" href="vectsp_2.html#T34" target="_self" title="VECTSP_2:th.34">Th34</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:38"/>
<font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">y</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_2"><b>proof </b></a><div class="add">

<a NAME="E1:38_2"/>
<font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font></span>)</span></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:38_2_1"/>
 <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">SF</font>
 
<b>by </b><i><a class="txt" href="vectsp_2.html#E1:38"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="vectsp_2.html#T34" target="_self" title="VECTSP_2:th.34">Th34</a></i>;<br/>
<b>hence </b><a NAME="E2:38_2_1"/>
<font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="vectsp_2.html#E3:38"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="vectsp_2.html#T53" target="_self" title="VECTSP_2:th.53">Th53</a></i>;<br/>


</div><b>end;</b></div>
<b>then </b><font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T40" title="VECTSP_1:th.40">VECTSP_1:40</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D13" title="VECTSP_1:def.13">VECTSP_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T40" title="VECTSP_1:th.40">VECTSP_1:40</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T41" title="VECTSP_1:th.41">VECTSP_1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30" title="RLVECT_1:th.30">RLVECT_1:30</a></i>
<br/>.= 
 <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">y</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D13" title="VECTSP_1:def.13">VECTSP_1:def 13</a>, <a class="txt" href="vectsp_2.html#E2:38"><i><font color="Green" title="E22">A2</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E3:38_2"/>
<font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">y</font></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:38"/>
<font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">y</font></span>)</span>
 ;<br/>


</div>
