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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E86">Th79</font></span>: <a NAME="T106"><span class="comment"><font color="firebrick">:: MSAFREE5:106</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">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="b3">X</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b4">x1</font>, <font color="Olive" title="b5">x2</font> being    <a href="msafree4.html#M1" title="MSAFREE4:mode.1">Element</a> of <font color="Olive" title="b3">X</font> <a href="msafree4.html#K1" title="MSAFREE4:func.1">.</a> <font color="Olive" title="b2">s</font><br/>  for <font color="Olive" title="b6">T</font> being  <font color="Olive">b<sub>3</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="msafree4.html#V8" title="MSAFREE4:attr.8">free_in_itself</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="b7">r</font> being   <a href="msafree3.html#NM1" title="MSAFREE3:NM.1">Element</a> of <font color="Olive" title="b6">T</font>  st <font color="Olive" title="b6">T</font> is  <a href="msafree5.html#V14" title="MSAFREE5:attr.14">struct-invariant</a>  &amp; <font color="Olive" title="b4">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">x2</font> &amp; <font color="Olive" title="b7">r</font> is <font color="Olive" title="b5">x2</font> <a href="msafree5.html#V9" title="MSAFREE5:attr.9">-omitting</a>  holds <br/><span class="p1">(<span class="default"><a href="msafree5.html#K22" title="MSAFREE5:func.22">Hom</a> (<font color="Olive" title="b6">T</font>,<font color="Olive" title="b4">x1</font>,<font color="Olive" title="b5">x2</font>)</span>)</span> <a href="msafree5.html#K4" title="MSAFREE5:func.4">.</a> <font color="Olive" title="b7">r</font> is <font color="Olive" title="b4">x1</font> <a href="msafree5.html#V9" title="MSAFREE5:attr.9">-omitting</a> </div></div>
