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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E28">Th20</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: BKMODEL4:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">N</font> being   <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of 3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a><br/>  for <font color="Olive" title="b2">h</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bkmodel2.html#K7" title="BKMODEL2:func.7">SubGroupK-isometry</a><br/>  for <font color="Olive" title="b3">n11</font>, <font color="Olive" title="b4">n12</font>, <font color="Olive" title="b5">n13</font>, <font color="Olive" title="b6">n21</font>, <font color="Olive" title="b7">n22</font>, <font color="Olive" title="b8">n23</font>, <font color="Olive" title="b9">n31</font>, <font color="Olive" title="b10">n32</font>, <font color="Olive" title="b11">n33</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a><br/>  for <font color="Olive" title="b12">P</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="bkmodel2.html#K1" title="BKMODEL2:func.1">BK_model</a> <br/>  for <font color="Olive" title="b13">u</font> being   non  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3</span>)</span>  st <font color="Olive" title="b2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_8.html#K4" title="ANPROJ_8:func.4">homography</a> <font color="Olive" title="b1">N</font> &amp; <font color="Olive" title="b1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b3">n11</font>,<font color="Olive" title="b4">n12</font>,<font color="Olive" title="b5">n13</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b6">n21</font>,<font color="Olive" title="b7">n22</font>,<font color="Olive" title="b8">n23</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b9">n31</font>,<font color="Olive" title="b10">n32</font>,<font color="Olive" title="b11">n33</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> &amp; <font color="Olive" title="b12">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Olive" title="b13">u</font> &amp; <font color="Olive" title="b13">u</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b9">n31</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b13">u</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b10">n32</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b13">u</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b11">n33</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>
