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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E52">Th33</font></span>: <a NAME="T33"><span class="comment"><font color="firebrick">:: GEOMTRAP:33</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">w</font>, <font color="Olive" title="b3">y</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b1">V</font>  st  <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Olive" title="b2">w</font>,<font color="Olive" title="b3">y</font> holds <br/> for <font color="Olive" title="b4">u</font>, <font color="Olive" title="b5">v</font>, <font color="Olive" title="b6">u1</font>, <font color="Olive" title="b7">v1</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b1">V</font> holds <br/> ( <font color="Olive" title="b4">u</font>,<font color="Olive" title="b5">v</font>,<font color="Olive" title="b6">u1</font>,<font color="Olive" title="b7">v1</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Olive" title="b2">w</font>,<font color="Olive" title="b3">y</font> iff  <a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> (<font color="Olive" title="b2">w</font>,<font color="Olive" title="b3">y</font>,<span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b4">u</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b7">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b6">u1</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )</div></div>
