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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="vectsp_2.html#NM3">Skew-Field</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><b>now </b></a><div class="add"><a NAME="E1:30_1"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="vectsp_2.html#K1" target="_self">"</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:30_1_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:30_1_1"/><b>then </b><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="vectsp_2.html#T39" target="_self">Th39</a></i>;<br/>
<a NAME="E3:30_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="vectsp_2.html#E1:30_1_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="vectsp_2.html#T41" target="_self">Th41</a></i>;<br/>
<b>hence </b><a NAME="E4:30_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="vectsp_2.html#K1" target="_self">"</a> 
 <b>by </b><i><a class="txt" href="vectsp_2.html#E2:30_1_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="vectsp_2.html#D7" target="_self">Def7</a></i>;<br/>


</div><b>end;</b></div><a NAME="E2:30_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="vectsp_2.html#K1" target="_self">"</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:30_1_2"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:30_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="vectsp_2.html#T39" target="_self">Th39</a></i>;<br/>
<b>hence </b><a NAME="E3:30_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="vectsp_2.html#K1" target="_self">"</a> 
 <b>by </b><i><a class="txt" href="vectsp_2.html#E1:30_1_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="vectsp_2.html#D7" target="_self">Def7</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:30_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font> implies ( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="vectsp_2.html#K1" target="_self">"</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="vectsp_2.html#K1" target="_self">"</a>  ) )
 <b>by </b><i><a class="txt" href="vectsp_2.html#E1:30_1"><i><font color="Green">E15</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:30"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font> implies ( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="vectsp_2.html#K1" target="_self">"</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="vectsp_2.html#K1" target="_self">"</a>  ) )
 ;<br/>


</div>
