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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th23</font></span>: <a NAME="T23"><span class="comment"><font color="firebrick">:: STIRL2_1:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">k</font>, <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  holds <br/> not <!--HUMANRECFAILED-->( ( <font color="Olive" title="b2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) &amp; ( <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies <font color="Olive" title="b2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) &amp; <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b1">k</font> &amp; (  for <font color="Olive" title="b3">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Olive" title="b2">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Olive" title="b1">k</font></span>)</span>  holds <br/>(  not <font color="Olive" title="b3">f</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  or  not <font color="Olive" title="b3">f</font> is  <a href="stirl2_1.html#V1" title="STIRL2_1:attr.1">"increasing</a>  ) ) )</div></div>
