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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E9">Th19</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: MSUALG_9:19</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>, <font color="Olive" title="b3">B</font>, <font color="Olive" title="b4">C</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="b5">F1</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">B</font><br/>  for <font color="Olive" title="b6">F2</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Olive" title="b2">A</font>,<font color="Olive" title="b4">C</font>  st <font color="Olive" title="b5">F1</font> <a href="msualg_3.html#R2" title="MSUALG_3:pred.2">is_epimorphism</a> <font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">B</font> &amp; <font color="Olive" title="b6">F2</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Olive" title="b2">A</font>,<font color="Olive" title="b4">C</font> holds <br/> for <font color="Olive" title="b7">G</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Olive" title="b3">B</font>,<font color="Olive" title="b4">C</font>  st <font color="Olive" title="b7">G</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <font color="Olive" title="b5">F1</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Olive" title="b6">F2</font> holds <br/><font color="Olive" title="b7">G</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Olive" title="b3">B</font>,<font color="Olive" title="b4">C</font></div></div>
