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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">v</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>;<br/>



<b>assume </b><a NAME="E1:34"/>
<font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">v</font>
 ;<br/>

<b>then </b> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">V</font> = 
<font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c2">v</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T28" target="_self" title="RLVECT_1:th.28">Th28</a></i>
<br/>.= 
<font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">v</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30" target="_self" title="RLVECT_1:th.30">Th30</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">v</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9" target="_self" title="RLVECT_1:def.9">Def9</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default">1 <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <font color="Maroon" title="c2">v</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9" target="_self" title="RLVECT_1:def.9">Def9</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <font color="Maroon" title="c2">v</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9" target="_self" title="RLVECT_1:def.9">Def9</a></i>
<br/>.= 
2 <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <font color="Maroon" title="c2">v</font>

;<br/>
<b>hence </b><a NAME="E3:34"/>
<font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T24" target="_self" title="RLVECT_1:th.24">Th24</a></i>;<br/>


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