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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E19">Th20</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: MATRTOP2:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">f</font> being  <font color="Olive">b<sub>1</sub></font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b4">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="b4">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/>( <font color="Olive" title="b3">f</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">B</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Olive" title="b2">k</font></span>)</span></span>)</span> iff <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> )</div></div>
