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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E7">Th5</font></span>: <a NAME="T5"><span class="comment"><font color="firebrick">:: OSALG_2:5</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">U0</font> being   <a href="osalg_1.html#NM5" title="OSALG_1:NM.5">OSAlgebra</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">U1</font> being    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Olive" title="b1">S</font> holds <br/> ( <font color="Olive" title="b3">U1</font> is   <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Olive" title="b2">U0</font> iff (  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b3">U1</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Olive" title="b2">U0</font> &amp; (  for <font color="Olive" title="b4">B</font> being    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Olive" title="b2">U0</font>  st <font color="Olive" title="b4">B</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b3">U1</font> holds <br/>( <font color="Olive" title="b4">B</font> is  <a href="msualg_2.html#V3" title="MSUALG_2:attr.3">opers_closed</a>  &amp;  the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Olive" title="b3">U1</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> (<font color="Olive" title="b2">U0</font>,<font color="Olive" title="b4">B</font>) ) ) ) )</div></div>
