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<div><span class="kw">theorem </span><a NAME="T36"><span class="comment"><font color="firebrick">:: REAL_NS2:36</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">F</font> being   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Olive" title="b1">n</font></span>)</span>  st  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b2">F</font> is  <a href="rlvect_3.html#V1" title="RLVECT_3:attr.1">linearly-independent</a>  holds <br/> for <font color="Olive" title="b3">B</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b1">n</font> <a href="prvect_1.html#K6" title="PRVECT_1:func.6">-VectSp_over</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st <font color="Olive" title="b3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix13.html#K11" title="MATRIX13:func.11">MX2FinS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>,<font color="Olive" title="b1">n</font>)</span>)</span> holds <br/> for <font color="Olive" title="b4">M</font> being   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of <font color="Olive" title="b1">n</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st <font color="Olive" title="b4">M</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Olive" title="b4">M</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">F</font> holds <br/><span class="p1">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Olive" title="b4">M</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <span class="p3">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p4">(<span class="default"><font color="Olive" title="b3">B</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">F</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="rlvect_3.html#K1" title="RLVECT_3:func.1">Lin</a> <span class="p2">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b2">F</font></span>)</span></span>)</span></div></div>
