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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">Th6</font></span>: <a NAME="T6"><span class="comment"><font color="firebrick">:: ANPROJ_2:6</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">o</font>, <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">u2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">u2</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">u</font> &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Olive" title="b2">o</font>,<font color="Olive" title="b4">u2</font> &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">u2</font> &amp; <font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">u2</font> <a href="anproj_2.html#R1" title="ANPROJ_2:pred.1">are_Prop_Vect</a>  holds <br/>(  ex <font color="Olive" title="b5">a1</font>, <font color="Olive" title="b6">b1</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>( <font color="Olive" title="b6">b1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b4">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">o</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">a1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b3">u</font></span>)</span> &amp; <font color="Olive" title="b5">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b6">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) &amp;  ex <font color="Olive" title="b5">a2</font>, <font color="Olive" title="b6">c2</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>( <font color="Olive" title="b4">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">c2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b2">o</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">a2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b3">u</font></span>)</span> &amp; <font color="Olive" title="b6">c2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b5">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) )</div></div>
