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

<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E1:8_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="normsp_1.html#V2" target="_self">RealNormSpace-like</a>
 <b>by </b><i><a class="ref" href="normsp_1.html#D2" target="_self">Def2</a>, <a class="txt" href="normsp_1.html#E11"><i><font color="Green">Lemma6</font></i></a></i>;<br/>

<a NAME="E2:8_1_1"/><i><font color="Green">E8</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font><br/>for <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">b<sub>4</sub></font> &amp; ( for <font color="Olive">b<sub>5</sub></font> being  <a href="real_1.html#NM1">Real</a> holds <font color="Olive">b<sub>5</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>5</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">b<sub>3</sub></font> ) )
 
;<br/>
<b>thus </b><a NAME="E3:8_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="rlvect_1.html#V7">RealLinearSpace-like</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:8_1_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a><br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>



<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="rlvect_1.html#NM1">VECTOR</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/>
<b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K3">*</a> <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> = 
<font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K3">*</a> <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>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K3">*</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>4</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>

;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:8_1_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a><br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font> holds <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="real_1.html#K3">+</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>





<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="rlvect_1.html#NM1">VECTOR</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K3">*</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="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>

;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:8_1_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a><br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font> holds <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="real_1.html#K4">*</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>





<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="rlvect_1.html#NM1">VECTOR</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>

<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>

;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="rlvect_1.html#NM1">VECTOR</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/>
<b>thus </b>1 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>4</sub></font> = 
1 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>

<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E4:8_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>1</sub></font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D5">RLVECT_1:def 5</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="rlvect_1.html#NM1">VECTOR</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/>
<b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>7</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="normsp_1.html#E2:8_1_1"><i><font color="Green">E8</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>4</sub></font>

;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E5:8_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font> holds <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>3</sub></font></span>)</span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="rlvect_1.html#NM1">VECTOR</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>6</sub></font> = 
<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> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font>

<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="rlvect_1.html#K4">+</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>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K2">+</a> <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>

;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E6:8_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font> holds <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="rlvect_1.html#NM1">VECTOR</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/>
<b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <span class="p2">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>
;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E7:8_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font>ex <font color="Olive">b<sub>2</sub></font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>3</sub></font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D8">RLVECT_1:def 8</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="rlvect_1.html#NM1">VECTOR</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="rlvect_1.html#NM1">VECTOR</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E3:8_1_1_5"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><a href="rlsub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D8">RLVECT_1:def 8</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/>
<b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/>

<b>thus </b><a NAME="E5:8_1_1_5"/>
<font color="Maroon">c<sub>4</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="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="normsp_1.html#E3:8_1_1_5"><i><font color="Green">E9</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E8:8_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="normsp_1.html#V1" target="_self">strict</a>
 ;<br/>


</div>
