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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E75">Th47</font></span>: <a NAME="T92"><span class="comment"><font color="firebrick">:: MSAFREE5:92</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> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msafree1.html#V1" title="MSAFREE1:attr.1">disjoint_valued</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">B</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="b4">o</font> being   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font> being    <a href="msafree4.html#M1" title="MSAFREE4:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Olive" title="b4">o</font>,<font color="Olive" title="b2">A</font>)<br/>  for <font color="Olive" title="b7">h</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="b8">a</font> being   <a href="msafree3.html#NM1" title="MSAFREE3:NM.1">Element</a> of <font color="Olive" title="b2">A</font><br/>  for <font color="Olive" title="b9">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b9">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b5">p</font> &amp; <font color="Olive" title="b6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">p</font> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</a> (<font color="Olive" title="b9">i</font>,<font color="Olive" title="b8">a</font>) holds <br/><font color="Olive" title="b7">h</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">h</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b5">p</font></span>)</span> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</a> (<font color="Olive" title="b9">i</font>,<span class="p1">(<span class="default"><font color="Olive" title="b7">h</font> <a href="msafree5.html#K4" title="MSAFREE5:func.4">.</a> <font color="Olive" title="b8">a</font></span>)</span>)</div></div>
