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<b>let </b><font color="Maroon">a</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:51"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font>
 <b>and </b><br/><a NAME="E2:51"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">a</font> <a href="rlvect_1.html#K3" target="_self">*</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="rlvect_1.html#K3" target="_self">*</a> <font color="Maroon">v</font>
 ;<br/>

 <a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K3" target="_self">*</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K6" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K3" target="_self">*</a> <font color="Maroon">v</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="real_1.html#K5">-</a> <font color="Maroon">b</font></span>)</span> <a href="rlvect_1.html#K3" target="_self">*</a> <font color="Maroon">v</font>
<b>by </b><i/>
;<br/>
<a NAME="E4:51"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="rlvect_1.html#E2:51"><i><font color="Green">E32</font></i></a>, </i>;<br/>
<a NAME="E5:51"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">b</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E6:51"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/>


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