<?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> be   <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:35"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">c<sub>1</sub></font> holds <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="vectsp_2.html#K2" target="_self">/</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="vectsp_2.html#K1" target="_self">"</a> 
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D19">VECTSP_1:def 19</a></i>;<br/>
<a NAME="E2:35"/>
( <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> implies <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="vectsp_2.html#K2" target="_self">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="vectsp_2.html#K1" target="_self">"</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:35_1"/><i><font color="Green">E20</font></i>: 
<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>
 ;<br/>

<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="vectsp_2.html#K2" target="_self">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="vectsp_2.html#K1" target="_self">"</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="vectsp_2.html#K1" target="_self">"</a> </span>)</span> <a href="vectsp_2.html#K1" target="_self">"</a> 
<b>by </b><i><a class="txt" href="vectsp_2.html#E1:35"><i><font color="Green">E19</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="vectsp_2.html#E1:35_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="vectsp_2.html#T49" target="_self">Th49</a></i>
;<br/>
<b>hence </b><a NAME="E3:35_1"/>
<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="vectsp_2.html#K2" target="_self">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="vectsp_2.html#K1" target="_self">"</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:35"/>
( <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> implies ( <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="vectsp_2.html#K2" target="_self">/</a> <font color="Maroon">c<sub>2</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>  &amp; <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="vectsp_2.html#K2" target="_self">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="vectsp_2.html#K1" target="_self">"</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> ) )
 <b>by </b><i><a class="txt" href="vectsp_2.html#E1:35"><i><font color="Green">E19</font></i></a></i>;<br/>


</div>
