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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E53">Th47</font></span>: <a NAME="T47"><span class="comment"><font color="firebrick">:: OSALG_2:47</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S1</font> being   <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</a><br/>  for <font color="Olive" title="b2">U0</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">S1</font> holds   <a href="osalg_2.html#K15" title="OSALG_2:func.15">OSAlg_meet</a> <font color="Olive" title="b2">U0</font> is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> </div></div>
