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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E57">Th45</font></span>: <a NAME="T45"><span class="comment"><font color="firebrick">:: IDEA_1:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">lk</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">Key</font> being   <a href="matrix_0.html#NM2" title="MATRIX_0:NM.2">Matrix</a> of <font color="Olive" title="b2">lk</font>,6,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a><br/>  for <font color="Olive" title="b4">r</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b5">M</font>, <font color="Olive" title="b6">m</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b5">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K3" title="FUNCT_7:func.3">compose</a> (<span class="p2">(<span class="default"><a href="idea_1.html#K17" title="IDEA_1:func.17">IDEA_P_F</a> (<font color="Olive" title="b3">Key</font>,<font color="Olive" title="b1">n</font>,<font color="Olive" title="b4">r</font>)</span>)</span>,<a href="idea_1.html#K14" title="IDEA_1:func.14">MESSAGES</a>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">m</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b6">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 &amp; <font color="Olive" title="b6">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b6">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b6">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b6">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 4 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> holds <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">M</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 &amp; <font color="Olive" title="b5">M</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b5">M</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b5">M</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b5">M</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 4 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Olive" title="b1">n</font> )</div></div>
