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<b>let </b><font color="Maroon">L</font> be    <a href="rmod_4.html#M1" target="_self">Linear_Combination</a> of <font color="Maroon">V</font>, <font color="Maroon">L'</font> be    <a href="rmod_4.html#M1" target="_self">Linear_Combination</a> of <font color="Maroon">V</font>;<br/>

<b>assume </b><a NAME="E1:60_1_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">L</font> <a href="rmod_4.html#R1" target="_self">=</a> <font color="Maroon">L'</font> <a href="rmod_4.html#K7" target="_self">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span></span>)</span>
 ;<br/>

<b>let </b><font color="Maroon">v</font> be   <a href="vectsp_2.html#NM5">Vector</a> of <font color="Maroon">V</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="rmod_4.html#D10" target="_self">RMOD_4:def 10</a><br/>

<b>thus </b><font color="Maroon">L'</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font> = 
<span class="p1">(<span class="default"><font color="Maroon">L'</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">L'</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">L'</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T42">VECTSP_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">L'</font> <a href="rmod_4.html#K7" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="rmod_4.html#K7" target="_self">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font>
<b>by </b><i>, </i>
;<br/>


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