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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E21">Def11</font></span>   defines <a href="mmlquer2.html#K10" title="MMLQUER2:func.10">order</a> <a onclick="hs(this)" href="javascript:()">MMLQUER2:def 11 : <br/></a><span> 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">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><br/>  for <font color="Olive" title="b3">S</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">b<sub>4</sub></font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mmlquer2.html#K10" title="MMLQUER2:func.10">order</a> (<font color="Olive" title="b3">S</font>,<font color="Olive" title="b2">R</font>) iff (  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">S</font> &amp; <font color="Olive">b<sub>4</sub></font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; (  for <font color="Olive" title="b5">i</font>, <font color="Olive" title="b6">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b5">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive" title="b6">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive">b<sub>4</sub></font> holds <br/>( <font color="Olive" title="b5">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b6">j</font> iff <font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font>,<font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">j</font> <a href="mmlquery.html#R1" title="MMLQUERY:pred.1">in</a> <font color="Olive" title="b2">R</font> ) ) ) );<br/></span></div>
