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<div><span class="kw">theorem </span><a NAME="T29"><span class="comment"><font color="firebrick">:: MSUALG_9:29</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</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="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">C</font> being   <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">MSCongruence</a> of <font color="Olive" title="b2">A</font>  st <font color="Olive" title="b3">C</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <span class="p1"><a href="pboole.html#K6" title="PBOOLE:func.6">[|</a><span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">A</font>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">A</font></span><a href="pboole.html#K6" title="PBOOLE:func.6">|]</a></span> holds <br/> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_4.html#K13" title="MSUALG_4:func.13">QuotMSAlg</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">C</font>)</span>)</span> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <span class="p1"><a href="pzfmisc1.html#K1" title="PZFMISC1:func.1">{</a><span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">A</font></span><a href="pzfmisc1.html#K1" title="PZFMISC1:func.1">}</a></span></div></div>
