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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E79">Th77</font></span>: <a NAME="T95"><span class="comment"><font color="firebrick">:: ANPROJ_8:95</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</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><br/>  for <font color="Olive" title="b4">M</font>, <font color="Olive" title="b5">PQR</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="b6">pf</font>, <font color="Olive" title="b7">qf</font>, <font color="Olive" title="b8">rf</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a><br/>  for <font color="Olive" title="b9">pt</font>, <font color="Olive" title="b10">qt</font>, <font color="Olive" title="b11">rt</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of 1 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <font color="Olive" title="b5">PQR</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"><span class="p3">(<span class="default"><font color="Olive" title="b1">p</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b2">q</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b3">r</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a></span>)</span></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"><span class="p3">(<span class="default"><font color="Olive" title="b1">p</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b2">q</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b3">r</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a></span>)</span></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"><span class="p3">(<span class="default"><font color="Olive" title="b1">p</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b2">q</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b3">r</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a></span>)</span></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="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">pf</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">qf</font> &amp; <font color="Olive" title="b3">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">rf</font> &amp; <font color="Olive" title="b9">pt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">M</font> <a href="laplace.html#K11" title="LAPLACE:func.11">*</a> <font color="Olive" title="b6">pf</font> &amp; <font color="Olive" title="b10">qt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">M</font> <a href="laplace.html#K11" title="LAPLACE:func.11">*</a> <font color="Olive" title="b7">qf</font> &amp; <font color="Olive" title="b11">rt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">M</font> <a href="laplace.html#K11" title="LAPLACE:func.11">*</a> <font color="Olive" title="b8">rf</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b4">M</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Olive" title="b5">PQR</font></span>)</span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a>  <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">(<span class="default"><a href="anproj_8.html#K2" title="ANPROJ_8:func.2">M2F</a> <font color="Olive" title="b9">pt</font></span>)</span>,<span class="p2">(<span class="default"><a href="anproj_8.html#K2" title="ANPROJ_8:func.2">M2F</a> <font color="Olive" title="b10">qt</font></span>)</span>,<span class="p2">(<span class="default"><a href="anproj_8.html#K2" title="ANPROJ_8:func.2">M2F</a> <font color="Olive" title="b11">rt</font></span>)</span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></div></div>
