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<div><span class="kw">theorem </span><a NAME="T15"><span class="comment"><font color="firebrick">:: NAT_2:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">k</font>, <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">k</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Olive" title="b3">n</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">n</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">k</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</div></div>
