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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E36">Th27</font></span>: <a NAME="T27"><span class="comment"><font color="firebrick">:: OSALG_1:27</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</a><br/>  for <font color="Olive" title="b2">A</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="osalg_1.html#NM5" title="OSALG_1:NM.5">OSAlgebra</a> of <font color="Olive" title="b1">S</font> holds <br/> ( <font color="Olive" title="b2">A</font> is  <a href="osalg_1.html#V13" title="OSALG_1:attr.13">monotone</a>  iff  for <font color="Olive" title="b3">o1</font>, <font color="Olive" title="b4">o2</font> being   <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b3">o1</font> <a href="osalg_1.html#R6" title="OSALG_1:pred.6">&lt;=</a> <font color="Olive" title="b4">o2</font> holds <br/> <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<font color="Olive" title="b3">o1</font>,<font color="Olive" title="b2">A</font>) <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<font color="Olive" title="b4">o2</font>,<font color="Olive" title="b2">A</font>) )</div></div>
