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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E51">Th20</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: PASCAL:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">MABF</font>, <font color="Olive" title="b2">MABE</font>, <font color="Olive" title="b3">MACF</font>, <font color="Olive" title="b4">MBDF</font>, <font color="Olive" title="b5">MCDE</font>, <font color="Olive" title="b6">MACE</font>, <font color="Olive" title="b7">MBDE</font>, <font color="Olive" title="b8">MCDF</font> being   <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="b9">p1</font>, <font color="Olive" title="b10">p2</font>, <font color="Olive" title="b11">p3</font>, <font color="Olive" title="b12">p4</font>, <font color="Olive" title="b13">p5</font>, <font color="Olive" title="b14">p6</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</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">MABE</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b9">p1</font>,<font color="Olive" title="b10">p2</font>,<font color="Olive" title="b13">p5</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> &amp; <font color="Olive" title="b3">MACF</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b9">p1</font>,<font color="Olive" title="b11">p3</font>,<font color="Olive" title="b14">p6</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> &amp; <font color="Olive" title="b4">MBDF</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b10">p2</font>,<font color="Olive" title="b12">p4</font>,<font color="Olive" title="b14">p6</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> &amp; <font color="Olive" title="b5">MCDE</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b11">p3</font>,<font color="Olive" title="b12">p4</font>,<font color="Olive" title="b13">p5</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> &amp; <font color="Olive" title="b1">MABF</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b9">p1</font>,<font color="Olive" title="b10">p2</font>,<font color="Olive" title="b14">p6</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> &amp; <font color="Olive" title="b6">MACE</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b9">p1</font>,<font color="Olive" title="b11">p3</font>,<font color="Olive" title="b13">p5</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> &amp; <font color="Olive" title="b7">MBDE</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b10">p2</font>,<font color="Olive" title="b12">p4</font>,<font color="Olive" title="b13">p5</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> &amp; <font color="Olive" title="b8">MCDF</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b11">p3</font>,<font color="Olive" title="b12">p4</font>,<font color="Olive" title="b14">p6</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> holds <br/>(  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Olive" title="b2">MABE</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Olive" title="b9">p1</font>,<font color="Olive" title="b10">p2</font>,<font color="Olive" title="b13">p5</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> &amp;  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Olive" title="b3">MACF</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Olive" title="b9">p1</font>,<font color="Olive" title="b11">p3</font>,<font color="Olive" title="b14">p6</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> &amp;  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Olive" title="b4">MBDF</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Olive" title="b10">p2</font>,<font color="Olive" title="b12">p4</font>,<font color="Olive" title="b14">p6</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> &amp;  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Olive" title="b5">MCDE</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Olive" title="b11">p3</font>,<font color="Olive" title="b12">p4</font>,<font color="Olive" title="b13">p5</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> &amp;  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Olive" title="b1">MABF</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Olive" title="b9">p1</font>,<font color="Olive" title="b10">p2</font>,<font color="Olive" title="b14">p6</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> &amp;  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Olive" title="b6">MACE</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Olive" title="b9">p1</font>,<font color="Olive" title="b11">p3</font>,<font color="Olive" title="b13">p5</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> &amp;  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Olive" title="b7">MBDE</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Olive" title="b10">p2</font>,<font color="Olive" title="b12">p4</font>,<font color="Olive" title="b13">p5</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> &amp;  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Olive" title="b8">MCDF</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Olive" title="b11">p3</font>,<font color="Olive" title="b12">p4</font>,<font color="Olive" title="b14">p6</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> )</div></div>
