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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E49">Th47</font></span>: <a NAME="T47"><span class="comment"><font color="firebrick">:: MSAFREE4:47</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">X</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>() <a href="struct_0.html#NM8" title="STRUCT_0:NM.8">ManySortedSet</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">A2</font> being  <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="msafree4.html#V5" title="MSAFREE4:attr.5">-terms</a>   <a href="msafree4.html#V6" title="MSAFREE4:attr.6">all_vars_including</a>   <a href="msafree4.html#V7" title="MSAFREE4:attr.7">inheriting_operations</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Olive" title="b1">S</font> holds <br/> (  <a href="msafree4.html#K4" title="MSAFREE4:func.4">canonical_homomorphism</a> <font color="Olive" title="b3">A2</font> <a href="msualg_3.html#R2" title="MSUALG_3:pred.2">is_epimorphism</a>  <a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> (<font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">X</font>),<font color="Olive" title="b3">A2</font> &amp; (  for <font color="Olive" title="b4">s</font> being   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b5">t</font> being   <a href="msualg_6.html#NM1" title="MSUALG_6:NM.1">Element</a> of <font color="Olive" title="b3">A2</font>,<font color="Olive" title="b4">s</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree4.html#K4" title="MSAFREE4:func.4">canonical_homomorphism</a> <font color="Olive" title="b3">A2</font></span>)</span> <a href="msafree4.html#K2" title="MSAFREE4:func.2">.</a> <font color="Olive" title="b4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">t</font> ) )</div></div>
