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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></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<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>











<b>assume </b><a NAME="E1:83"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="circtrm1.html#R5" target="_self">are_similar_wrt</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:83"/><b>then </b><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="circtrm1.html#R5" target="_self">are_similar_wrt</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K2">"</a> ,<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K2">"</a> 
 
<b>by </b><i><a class="ref" href="circtrm1.html#T40" target="_self">Th40</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">c<sub>5</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">c<sub>6</sub></font>;<br/>



<b>assume </b><a NAME="E3:83"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E4:83"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K2">"</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="circtrm1.html#E1:83"><i><font color="Green">E57</font></i></a>, <a class="txt" href="circtrm1.html#E3:83"><i><font color="Green">E59</font></i></a>, <a class="ref" href="circtrm1.html#T52" target="_self">Th52</a></i>;<br/>
<b>thus </b><a NAME="E5:83"/>
( <font color="Maroon">c<sub>7</sub></font> is <a href="circuit2.html#V1">stable</a> implies <font color="Maroon">c<sub>8</sub></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">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="circuit2.html#K6">Following</a> <font color="Maroon">c<sub>7</sub></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">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="circuit2.html#K6">Following</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="circtrm1.html#E2:83"><i><font color="Green">E58</font></i></a>, <a class="txt" href="circtrm1.html#E4:83"><i><font color="Green">E60</font></i></a>, <a class="ref" href="circtrm1.html#T55" target="_self">Th55</a></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">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="circuit2.html#K6">Following</a> <font color="Maroon">c<sub>8</sub></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">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="circuit2.html#K6">Following</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="circtrm1.html#E1:83"><i><font color="Green">E57</font></i></a>, <a class="txt" href="circtrm1.html#E3:83"><i><font color="Green">E59</font></i></a>, <a class="ref" href="circtrm1.html#T55" target="_self">Th55</a></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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