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<span class="kw">let </span><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b3">C1</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="Maroon" title="c1">G1</font><br/>  for <font color="Olive" title="b4">C2</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="Maroon" title="c2">G2</font>  st <font color="Olive" title="b3">C1</font>,<font color="Olive" title="b4">C2</font> <a href="circtrm1.html#R5" title="CIRCTRM1:pred.5">are_similar_wrt</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> holds <br/> for <font color="Olive" title="b5">s1</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b3">C1</font><br/>  for <font color="Olive" title="b6">s2</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b4">C2</font>  st <font color="Olive" title="b5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">s2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b1">f</font> holds <br/>( <font color="Olive" title="b5">s1</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  iff <font color="Olive" title="b6">s2</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">C1</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="Maroon" title="c1">G1</font><br/>  for <font color="Olive" title="b2">C2</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="Maroon" title="c2">G2</font>  st <font color="Olive" title="b1">C1</font>,<font color="Olive" title="b2">C2</font> <a href="circtrm1.html#R5" title="CIRCTRM1:pred.5">are_similar_wrt</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font> holds <br/> for <font color="Olive" title="b3">s1</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b1">C1</font><br/>  for <font color="Olive" title="b4">s2</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b2">C2</font>  st <font color="Olive" title="b3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">s2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">f</font> holds <br/>( <font color="Olive" title="b3">s1</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  iff <font color="Olive" title="b4">s2</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">C1</font> be   <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="Maroon" title="c1">G1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">C2</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="Maroon" title="c2">G2</font>  st <font color="Maroon" title="c5">C1</font>,<font color="Olive" title="b1">C2</font> <a href="circtrm1.html#R5" title="CIRCTRM1:pred.5">are_similar_wrt</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font> holds <br/> for <font color="Olive" title="b2">s1</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">C1</font><br/>  for <font color="Olive" title="b3">s2</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b1">C2</font>  st <font color="Olive" title="b2">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">f</font> holds <br/>( <font color="Olive" title="b2">s1</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  iff <font color="Olive" title="b3">s2</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">C2</font> be   <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="Maroon" title="c2">G2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">C1</font>,<font color="Maroon" title="c6">C2</font> <a href="circtrm1.html#R5" title="CIRCTRM1:pred.5">are_similar_wrt</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font> implies  for <font color="Olive" title="b1">s1</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">C1</font><br/>  for <font color="Olive" title="b2">s2</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">C2</font>  st <font color="Olive" title="b1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">f</font> holds <br/>( <font color="Olive" title="b1">s1</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  iff <font color="Olive" title="b2">s2</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  ) )</span><br/>











<span class="kw">assume </span><a NAME="E1:74"/><span class="lab"><font color="Green" title="E51">A1</font></span>: 
<font color="Maroon" title="c5">C1</font>,<font color="Maroon" title="c6">C2</font> <a href="circtrm1.html#R5" title="CIRCTRM1:pred.5">are_similar_wrt</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s1</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">C1</font><br/>  for <font color="Olive" title="b2">s2</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">C2</font>  st <font color="Olive" title="b1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">f</font> holds <br/>( <font color="Olive" title="b1">s1</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  iff <font color="Olive" title="b2">s2</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  )</span><br/>

<a NAME="E2:74"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A2</font></span>: 
<font color="Maroon" title="c6">C2</font>,<font color="Maroon" title="c5">C1</font> <a href="circtrm1.html#R5" title="CIRCTRM1:pred.5">are_similar_wrt</a> <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> ,<font color="Maroon" title="c4">g</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#T39" target="_self" onmouseover="rs('circtrm1/T39')" onmouseout="rh()">Th39</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c7">s1</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">C1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s2</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">C2</font>  st <font color="Maroon" title="c7">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">f</font> holds <br/>( <font color="Maroon" title="c7">s1</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  iff <font color="Olive" title="b1">s2</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">s2</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">C2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">f</font> implies ( <font color="Maroon" title="c7">s1</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  iff <font color="Maroon" title="c8">s2</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  ) )</span><br/>



<span class="kw">assume </span><a NAME="E3:74"/><span class="lab"><font color="Green" title="E53">A3</font></span>: 
<font color="Maroon" title="c7">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">f</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">s1</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  iff <font color="Maroon" title="c8">s2</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  )</span><br/>

<a NAME="E4:74"/><span class="lab"><font color="Green" title="E54">A4</font></span>: 
<font color="Maroon" title="c8">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s1</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="txt" href="#E3:74"><span class="lab"><font color="Green" title="E53">A3</font></span></a>, <a class="ref" href="circtrm1.html#T51" target="_self" onmouseover="rs('circtrm1/T51')" onmouseout="rh()">Th51</a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:74"/>
( <font color="Maroon" title="c7">s1</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  implies <font color="Maroon" title="c8">s2</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E52">A2</font></span></a>, <a class="txt" href="#E4:74"><span class="lab"><font color="Green" title="E54">A4</font></span></a>, <a class="ref" href="circtrm1.html#T54" target="_self" onmouseover="rs('circtrm1/T54')" onmouseout="rh()">Th54</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">s2</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  implies <font color="Maroon" title="c7">s1</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E6:74"/>
<font color="Maroon" title="c8">s2</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c8">s2</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="circuit2.html#D6" onmouseover="rs('circuit2/D6')" onmouseout="rh()">CIRCUIT2:def 6</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">s1</font> is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a> </span><br/>

<span class="kw">hence </span><a NAME="E7:74"/>
<font color="Maroon" title="c7">s1</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c7">s1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="txt" href="#E3:74"><span class="lab"><font color="Green" title="E53">A3</font></span></a>, <a class="ref" href="circtrm1.html#T54" target="_self" onmouseover="rs('circtrm1/T54')" onmouseout="rh()">Th54</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="circuit2.html#D6" onmouseover="rs('circuit2/D6')" onmouseout="rh()">CIRCUIT2:def 6</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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