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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th10</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: ENDALG:10</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">U1</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">x</font>, <font color="Olive" title="b4">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="endalg.html#K6" title="ENDALG:func.6">MSAEndMonoid</a> <font color="Olive" title="b2">U1</font></span>)</span><br/>  for <font color="Olive" title="b5">f</font>, <font color="Olive" title="b6">g</font> being    <a href="autalg_1.html#M1" title="AUTALG_1:mode.1">Element</a> of  <a href="endalg.html#K4" title="ENDALG:func.4">MSAEnd</a> <font color="Olive" title="b2">U1</font>  st <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">f</font> &amp; <font color="Olive" title="b4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">g</font> holds <br/><font color="Olive" title="b3">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">g</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <font color="Olive" title="b5">f</font></div></div>
