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<div><span class="kw">theorem </span><a NAME="T43"><span class="comment"><font color="firebrick">:: MSATERM:43</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="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">V</font> being    <a href="msaterm.html#M4" title="MSATERM:mode.4">Variables</a> of <font color="Olive" title="b2">A</font><br/>  for <font color="Olive" title="b4">f</font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <font color="Olive" title="b3">V</font>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">A</font><br/>  for <font color="Olive" title="b5">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="b6">p</font> being   <a href="msaterm.html#NM4" title="MSATERM:NM.4">ArgumentSeq</a> of <font color="Olive" title="b5">o</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">V</font><br/>  for <font color="Olive" title="b7">q</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b7">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b6">p</font> &amp; (  for <font color="Olive" title="b8">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b8">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="b6">p</font> holds <br/> for <font color="Olive" title="b9">t</font> being   <a href="msaterm.html#NM3" title="MSATERM:NM.3">c-Term</a> of <font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">V</font>  st <font color="Olive" title="b9">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b8">i</font> holds <br/><font color="Olive" title="b7">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b9">t</font> <a href="msaterm.html#K9" title="MSATERM:func.9">@</a> <font color="Olive" title="b4">f</font> ) holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msaterm.html#K2" title="MSATERM:func.2">Sym</a> (<font color="Olive" title="b5">o</font>,<span class="p3">(<span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">A</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Olive" title="b3">V</font></span>)</span>)</span>)</span> <a href="msaterm.html#K6" title="MSATERM:func.6">-tree</a> <font color="Olive" title="b6">p</font></span>)</span> <a href="msaterm.html#K9" title="MSATERM:func.9">@</a> <font color="Olive" title="b4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> (<font color="Olive" title="b5">o</font>,<font color="Olive" title="b2">A</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b7">q</font></div></div>
