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<div><span class="kw">theorem </span><a NAME="T22"><span class="comment"><font color="firebrick">:: CIRCTRM1:22</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="msafree2.html#V4" title="MSAFREE2:attr.4">finite-yielding</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">X</font> being    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b3">V</font>  st (  for <font color="Olive" title="b5">t</font> being   <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b3">V</font><br/>  for <font color="Olive" title="b6">o</font> being   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Olive" title="b1">S</font>  holds <br/>(  not <font color="Olive" title="b5">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Olive" title="b4">X</font> or  not <font color="Olive" title="b5">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b6">o</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">S</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or  not  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Olive" title="b6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) ) holds <br/> for <font color="Olive" title="b5">s</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Olive" title="b4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Olive" title="b2">A</font></span>)</span><br/>  for <font color="Olive" title="b6">f</font> being    <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Olive" title="b5">s</font><br/>  for <font color="Olive" title="b7">t</font> being   <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b3">V</font>  st <font color="Olive" title="b7">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Olive" title="b4">X</font> holds <br/>(  <a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> (<font color="Olive" title="b5">s</font>,<span class="p1">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b7">t</font></span>)</span></span>)</span>) <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Olive" title="b7">t</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> (<font color="Olive" title="b5">s</font>,<span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b7">t</font></span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b7">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> (<font color="Olive" title="b6">f</font>,<font color="Olive" title="b2">A</font>) )</div></div>
