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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="msafree2.html#V4" title="MSAFREE2:attr.4">locally-finite</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c3">V</font> be    <a href="msaterm.html#M4" title="MSATERM:mode.4">Variables</a> of <font color="Maroon" title="c2">A</font>;<br/><b>let </b><font color="Maroon" title="c4">X</font> be    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">V</font>;<br/><b>let </b><font color="Maroon" title="c5">G</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon" title="c6">C</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c5">G</font>;<br/>











<b>assume </b><a NAME="E1:90"/>
<font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font> <a href="circtrm1.html#R8" title="CIRCTRM1:pred.8">specifies</a> <font color="Maroon" title="c6">C</font>
 ;<br/>

<a NAME="E2:90"/><b>then </b>
<font color="Maroon" title="c6">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="circtrm1.html#T59" target="_self" title="CIRCTRM1:th.59">Th59</a></i>;<br/>
<b>hence </b><a NAME="E3:90"/>
for <font color="Olive" title="b1">t</font> being  <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">V</font>  st <font color="Olive" title="b1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c4">X</font> holds <br/> ex <font color="Olive" title="b2">v</font> being  <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <font color="Maroon" title="c5">G</font> st <br/>for <font color="Olive" title="b3">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">C</font> holds <br/> (  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b3">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <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#K1" title="RELAT_1:func.1">dom</a> <font color="Olive" title="b1">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Olive" title="b2">v</font> &amp;  ex <font color="Olive" title="b4">f</font> being   <a href="circtrm1.html#M2" title="CIRCTRM1:mode.2">SortMap</a> of <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c6">C</font> st <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="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font></span>)</span>  st <font color="Olive" title="b5">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b4">f</font> holds <br/>for <font color="Olive" title="b6">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Olive" title="b5">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b3">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Olive" title="b1">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b6">h</font>,<font color="Maroon" title="c2">A</font> )
 <b>by </b><i><a class="ref" href="circtrm1.html#T61" target="_self" title="CIRCTRM1:th.61">Th61</a></i>;<br/>


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