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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>let </b><font color="Maroon" title="c3">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c4">v</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c3">V</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:51"/><i><font color="Green" title="E32">A1</font></i>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c3">V</font>
 <b>and </b><br/><a NAME="E2:51"/><i><font color="Green" title="E33">A2</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <font color="Maroon" title="c4">v</font>
 ;<br/>

 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c3">V</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <font color="Maroon" title="c4">v</font></span>)</span>
<b>by </b><i><a class="txt" href="rlvect_1.html#E2:51"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="rlvect_1.html#T28" target="_self" title="RLVECT_1:th.28">Th28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <font color="Maroon" title="c4">v</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T49" target="_self" title="RLVECT_1:th.49">Th49</a></i>
;<br/>
<a NAME="E4:51"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="txt" href="rlvect_1.html#E1:51"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="rlvect_1.html#T24" target="_self" title="RLVECT_1:th.24">Th24</a></i>;<br/>
<a NAME="E5:51"/><b>then </b>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c2">b</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E6:51"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font>
 ;<br/>


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