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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: MSUALG_6:18</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">s1</font>, <font color="Olive" title="b4">s2</font>, <font color="Olive" title="b5">s3</font> being   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Olive" title="b1">S</font>  st  <a href="msualg_6.html#K3" title="MSUALG_6:func.3">TranslationRel</a> <font color="Olive" title="b1">S</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Olive" title="b3">s1</font>,<font color="Olive" title="b4">s2</font> &amp;  <a href="msualg_6.html#K3" title="MSUALG_6:func.3">TranslationRel</a> <font color="Olive" title="b1">S</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Olive" title="b4">s2</font>,<font color="Olive" title="b5">s3</font> holds <br/> for <font color="Olive" title="b6">t1</font> being    <a href="msualg_6.html#M2" title="MSUALG_6:mode.2">Translation</a> of <font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">s1</font>,<font color="Olive" title="b4">s2</font><br/>  for <font color="Olive" title="b7">t2</font> being    <a href="msualg_6.html#M2" title="MSUALG_6:mode.2">Translation</a> of <font color="Olive" title="b2">A</font>,<font color="Olive" title="b4">s2</font>,<font color="Olive" title="b5">s3</font> holds  <font color="Olive" title="b7">t2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b6">t1</font> is    <a href="msualg_6.html#M2" title="MSUALG_6:mode.2">Translation</a> of <font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">s1</font>,<font color="Olive" title="b5">s3</font></div></div>
