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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th16</font></span>: <a NAME="T16"><span class="comment"><font color="firebrick">:: CIRCUIT2:16</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">IIG</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>   <a href="msafree2.html#V5" title="MSAFREE2:attr.5">monotonic</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/>  for <font color="Olive" title="b2">SCS</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Olive" title="b1">IIG</font><br/>  for <font color="Olive" title="b3">InpFs</font> being   <a href="circuit1.html#NM2" title="CIRCUIT1:NM.2">InputFuncs</a> of <font color="Olive" title="b2">SCS</font>  st  <a href="funct_6.html#K9" title="FUNCT_6:func.9">commute</a> <font color="Olive" title="b3">InpFs</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  &amp;  not  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Olive" title="b1">IIG</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  holds <br/> for <font color="Olive" title="b4">s</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b2">SCS</font><br/>  for <font color="Olive" title="b5">iv</font> being    <a href="msafree2.html#M1" title="MSAFREE2:mode.1">InputValues</a> of <font color="Olive" title="b2">SCS</font>  st <font color="Olive" title="b5">iv</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funct_6.html#K9" title="FUNCT_6:func.9">commute</a> <font color="Olive" title="b3">InpFs</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> holds <br/> for <font color="Olive" title="b6">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b7">v</font> being   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <font color="Olive" title="b1">IIG</font>  st  <a href="circuit1.html#K6" title="CIRCUIT1:func.6">depth</a> (<font color="Olive" title="b7">v</font>,<font color="Olive" title="b2">SCS</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b6">k</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="circuit2.html#K9" title="CIRCUIT2:func.9">Computation</a> (<font color="Olive" title="b4">s</font>,<font color="Olive" title="b3">InpFs</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b7">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circuit2.html#K5" title="CIRCUIT2:func.5">IGValue</a> (<font color="Olive" title="b7">v</font>,<font color="Olive" title="b5">iv</font>)</div></div>
