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<div><span class="kw">theorem </span><a NAME="T39"><span class="comment"><font color="firebrick">:: RLVECT_4:39</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a><br/>  for <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v2</font>, <font color="Olive" title="b4">v3</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b5">a</font>, <font color="Olive" title="b6">b</font>, <font color="Olive" title="b7">c</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b2">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">v2</font> &amp; <font color="Olive" title="b2">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">v3</font> &amp; <font color="Olive" title="b3">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">v3</font> holds <br/> ex <font color="Olive" title="b8">l</font> being    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font>,<font color="Olive" title="b4">v3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> st <br/>( <font color="Olive" title="b8">l</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a</font> &amp; <font color="Olive" title="b8">l</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">b</font> &amp; <font color="Olive" title="b8">l</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">v3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">c</font> ) <span class="kw">by</span> <span class="lab"><a class="txt" href="rlvect_4.html#E3"><span class="lab"><font color="Green" title="E3">Lm3</font></span></a></span>;<br/></div></div>
