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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E4">Th4</font></span>: <a NAME="T5"><span class="comment"><font color="firebrick">:: BAGORDER:5</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b1">n</font> holds <br/> ( <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b</font> iff ( (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p1">(<span class="default"><font color="Olive" title="b2">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="bagorder.html#K1" title="BAGORDER:func.1">-cut</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p1">(<span class="default"><font color="Olive" title="b2">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="bagorder.html#K1" title="BAGORDER:func.1">-cut</a> <font color="Olive" title="b4">b</font> &amp; (<span class="p1">(<span class="default"><font color="Olive" title="b2">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Olive" title="b1">n</font>) <a href="bagorder.html#K1" title="BAGORDER:func.1">-cut</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Olive" title="b1">n</font>) <a href="bagorder.html#K1" title="BAGORDER:func.1">-cut</a> <font color="Olive" title="b4">b</font> ) )</div></div>
