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<div><span class="kw">theorem </span><a NAME="T21"><span class="comment"><font color="firebrick">:: MMLQUER2:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">S1</font>, <font color="Olive" title="b3">S2</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b4">R</font> being   <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>  <a href="orders_1.html#NM4" title="ORDERS_1:NM.4">Order</a> of <font color="Olive" title="b1">X</font> holds <br/> (  <a href="mmlquer2.html#K10" title="MMLQUER2:func.10">order</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">S1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">S2</font></span>)</span>,<font color="Olive" title="b4">R</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="mmlquer2.html#K10" title="MMLQUER2:func.10">order</a> (<font color="Olive" title="b2">S1</font>,<font color="Olive" title="b4">R</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><a href="mmlquer2.html#K10" title="MMLQUER2:func.10">order</a> (<font color="Olive" title="b3">S2</font>,<font color="Olive" title="b4">R</font>)</span>)</span> iff  for <font color="Olive" title="b5">x</font>, <font color="Olive" title="b6">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">S1</font> &amp; <font color="Olive" title="b6">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">S2</font> holds <br/>( <font color="Olive" title="b5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">y</font> &amp; <font color="Olive" title="b5">x</font>,<font color="Olive" title="b6">y</font> <a href="mmlquery.html#R1" title="MMLQUERY:pred.1">in</a> <font color="Olive" title="b4">R</font> ) )</div></div>
