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<b>let </b><font color="Maroon">G1</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">G2</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">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">C1</font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">C2</font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">G2</font>;<br/>











<b>assume </b><a NAME="E1:83"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">C1</font>,<font color="Maroon">C2</font> <a href="circtrm1.html#R5" target="_self">are_similar_wrt</a> <font color="Maroon">f</font>,<font color="Maroon">g</font>
 ;<br/>

<a NAME="E2:83"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">C2</font>,<font color="Maroon">C1</font> <a href="circtrm1.html#R5" target="_self">are_similar_wrt</a> <font color="Maroon">f</font> <a href="funct_1.html#K2">"</a> ,<font color="Maroon">g</font> <a href="funct_1.html#K2">"</a> 
 
<b>by </b><i/>;<br/>
<b>let </b><font color="Maroon">s1</font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">C1</font>;<br/><b>let </b><font color="Maroon">s2</font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">C2</font>;<br/>



<b>assume </b><a NAME="E3:83"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font>
 ;<br/>

<a NAME="E4:83"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K2">"</a> </span>)</span>
 
<b>by </b><i>, , </i>;<br/>
<b>thus </b><a NAME="E5:83"/>
( <font color="Maroon">s1</font> is <a href="circuit2.html#V1">stable</a> implies <font color="Maroon">s2</font> is <a href="circuit2.html#V1">stable</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:83_1"/>
<font color="Maroon">s1</font> <a href="hidden.html#R1">=</a>  <a href="circuit2.html#K6">Following</a> <font color="Maroon">s1</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circuit2.html#D6">CIRCUIT2:def 6</a><br/>

<b>hence </b><a NAME="E2:83_1"/>
<font color="Maroon">s2</font> <a href="hidden.html#R1">=</a>  <a href="circuit2.html#K6">Following</a> <font color="Maroon">s2</font>
 <b>by </b><i>, , </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="circuit2.html#D6">CIRCUIT2:def 6</a><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E6:83"/>
<font color="Maroon">s2</font> <a href="hidden.html#R1">=</a>  <a href="circuit2.html#K6">Following</a> <font color="Maroon">s2</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circuit2.html#D6">CIRCUIT2:def 6</a><br/>

<b>hence </b><a NAME="E7:83"/>
<font color="Maroon">s1</font> <a href="hidden.html#R1">=</a>  <a href="circuit2.html#K6">Following</a> <font color="Maroon">s1</font>
 <b>by </b><i>, , </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="circuit2.html#D6">CIRCUIT2:def 6</a><br/>


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