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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">A</font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="msafree2.html#V4">locally-finite</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">V</font> be    <a href="msaterm.html#M4">Variables</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">X</font> be    <a href="msaterm.html#M3">SetWithCompoundTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">G</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a> <a href="msafree2.html#V2">Circuit-like</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">C</font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">G</font>;<br/>











<b>assume </b><a NAME="E1:90"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">C</font> <a href="circtrm1.html#R7" target="_self">calculates</a> <font color="Maroon">X</font>,<font color="Maroon">A</font>
 ;<br/>

<b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E3:90"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">f</font>,<font color="Maroon">g</font> <a href="circtrm1.html#R4" target="_self">form_embedding_of</a> <font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font>,<font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E4:90"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">f</font> <a href="circtrm1.html#R3" target="_self">preserves_inputs_of</a> <font color="Maroon">X</font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a> ,<font color="Maroon">G</font>
 <b>by </b><i/>;<br/>
<a NAME="E5:90"/>
<font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="circtrm1.html#T8" target="_self">Th8</a>, </i>;<br/>
<b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as    <a href="circtrm1.html#M2" target="_self">SortMap</a> of <font color="Maroon">X</font>,<font color="Maroon">A</font>,<font color="Maroon">C</font> <b>by </b><i>, <a class="ref" href="circtrm1.html#T8" target="_self">Th8</a>, , </i>;<br/>
<b>let </b><font color="Maroon">t</font> be   <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font>;<br/>

<b>assume </b><a NAME="E7:90"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="trees_9.html#K9">Subtrees</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E8:90"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">f</font>,<font color="Maroon">g</font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">X</font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a> ,<font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="circtrm1.html#T8" target="_self">Th8</a>, </i>;<br/>
<b>reconsider </b><font color="Maroon">t'</font> = <font color="Maroon">t</font> as   <a href="msafree2.html#NM1">Vertex</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a> </span>)</span> <b>by </b><i><a class="txt" href="circtrm1.html#E7:90"><i><font color="Green">E65</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">v</font> = <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">t'</font> as   <a href="msafree2.html#NM1">Vertex</a> of <font color="Maroon">G</font> <b>by </b><i><a class="ref" href="circtrm1.html#T9" target="_self">Th9</a>, </i>;<br/>
<b>take </b>
<font color="Maroon">v</font>
;<br/>

<b>let </b><font color="Maroon">s</font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">C</font>;<br/>

<b>thus </b><a NAME="E11:90"/>
 <a href="facirc_1.html#K9">Following</a> <font color="Maroon">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1">is_stable_at</a> <font color="Maroon">v</font>
 <b>by </b><i>, </i>;<br/>

<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>thus </b><a NAME="E12:90"/>
for <font color="Olive">s'</font> being  <a href="circuit1.html#NM3">State</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="circtrm1.html#K6" target="_self">-Circuit</a> <font color="Maroon">A</font></span>)</span>  st <font color="Olive">s'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font> holds <br/>for <font color="Olive">h</font> being   <a href="circtrm1.html#M1" target="_self">CompatibleValuation</a> of <font color="Olive">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="circtrm1.html#K7" target="_self">@</a> <font color="Olive">h</font>,<font color="Maroon">A</font>
 <b>by </b><i>, </i>;<br/>


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