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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E55">Th39</font></span>: <a NAME="T39"><span class="comment"><font color="firebrick">:: MATRTOP3:39</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">f1</font>, <font color="Olive" title="b4">f2</font> being   <a href="vectsp_1.html#V13" title="VECTSP_1:attr.13">additive</a>   <a href="topreal9.html#V1" title="TOPREAL9:attr.1">homogeneous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b2">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b2">n</font></span>)</span>  st <font color="Olive" title="b3">f1</font> is  <a href="matrtop3.html#V2" title="MATRTOP3:attr.2">rotation</a>  &amp;  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrtop3.html#K3" title="MATRTOP3:func.3">AutMt</a> <font color="Olive" title="b3">f1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a></span>)</span> &amp; <font color="Olive" title="b1">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b2">n</font> &amp;  <a href="matrtop3.html#K3" title="MATRTOP3:func.3">AutMt</a> <font color="Olive" title="b4">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrtop3.html#K1" title="MATRTOP3:func.1">AxialSymmetry</a> (<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">n</font>) holds <br/><font color="Olive" title="b3">f1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">f2</font> is  <a href="matrtop3.html#V3" title="MATRTOP3:attr.3">base_rotation</a> </div></div>
