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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th19</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: MATRTOP3:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b2">i</font>, <font color="Olive" title="b3">j</font>, <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">i</font> &amp; <font color="Olive" title="b2">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">j</font> &amp; <font color="Olive" title="b3">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">n</font> holds <br/>(  <a href="matrtop3.html#K2" title="MATRTOP3:func.2">Rotation</a> (<font color="Olive" title="b2">i</font>,<font color="Olive" title="b3">j</font>,<font color="Olive" title="b4">n</font>,<font color="Olive" title="b1">r</font>) is  <a href="matrix_6.html#V4" title="MATRIX_6:attr.4">Orthogonal</a>  &amp; <span class="p1">(<span class="default"><a href="matrtop3.html#K2" title="MATRTOP3:func.2">Rotation</a> (<font color="Olive" title="b2">i</font>,<font color="Olive" title="b3">j</font>,<font color="Olive" title="b4">n</font>,<font color="Olive" title="b1">r</font>)</span>)</span> <a href="matrix_6.html#K1" title="MATRIX_6:func.1">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrtop3.html#K2" title="MATRTOP3:func.2">Rotation</a> (<font color="Olive" title="b2">i</font>,<font color="Olive" title="b3">j</font>,<font color="Olive" title="b4">n</font>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Olive" title="b1">r</font></span>)</span>) )</div></div>
