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<div><span class="kw">theorem </span><a NAME="T38"><span class="comment"><font color="firebrick">:: MSAFREE4:38</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">A</font>, <font color="Olive" title="b4">B</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <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="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Olive" title="b1">S</font>  st  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b3">A</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Olive" title="b3">A</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(#  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b4">B</font>, the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Olive" title="b4">B</font> #) holds <br/>( ( <font color="Olive" title="b3">A</font> is  <a href="msafree4.html#V6" title="MSAFREE4:attr.6">all_vars_including</a>  implies <font color="Olive" title="b4">B</font> is  <a href="msafree4.html#V6" title="MSAFREE4:attr.6">all_vars_including</a>  ) &amp; ( <font color="Olive" title="b3">A</font> is  <a href="msafree4.html#V7" title="MSAFREE4:attr.7">inheriting_operations</a>  implies <font color="Olive" title="b4">B</font> is  <a href="msafree4.html#V7" title="MSAFREE4:attr.7">inheriting_operations</a>  ) &amp; ( <font color="Olive" title="b3">A</font> is  <a href="msafree4.html#V8" title="MSAFREE4:attr.8">free_in_itself</a>  implies <font color="Olive" title="b4">B</font> is  <a href="msafree4.html#V8" title="MSAFREE4:attr.8">free_in_itself</a>  ) )</div></div>
