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<div><span class="kw">theorem </span><a NAME="T44"><span class="comment"><font color="firebrick">:: IDEA_1:44</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> holds <br/> (  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</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#K18" title="IDEA_1:func.18">IDEA_Q_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="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="idea_1.html#K14" title="IDEA_1:func.14">MESSAGES</a>  &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</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#K18" title="IDEA_1:func.18">IDEA_Q_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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K14" title="IDEA_1:func.14">MESSAGES</a>  )</div></div>
