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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E10">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: OSALG_3:12</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">U1</font>, <font color="Olive" title="b3">U2</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><br/>  for <font color="Olive" title="b4">F</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Olive" title="b2">U1</font>,<font color="Olive" title="b3">U2</font>  st <font color="Olive" title="b4">F</font> is  <a href="osalg_3.html#V1" title="OSALG_3:attr.1">order-sorted</a>  holds <br/> for <font color="Olive" title="b5">o1</font>, <font color="Olive" title="b6">o2</font> being   <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Olive" title="b1">S1</font>  st <font color="Olive" title="b5">o1</font> <a href="osalg_1.html#R6" title="OSALG_1:pred.6">&lt;=</a> <font color="Olive" title="b6">o2</font> holds <br/> for <font color="Olive" title="b7">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Olive" title="b5">o1</font>,<font color="Olive" title="b2">U1</font>)<br/>  for <font color="Olive" title="b8">x1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Olive" title="b6">o2</font>,<font color="Olive" title="b2">U1</font>)  st <font color="Olive" title="b7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">x1</font> holds <br/><font color="Olive" title="b4">F</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">F</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b8">x1</font></div></div>
