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<span class="kw">let </span><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="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">A</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">S</font><br/>  for <font color="Olive" title="b2">s</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b3">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st  <a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> (<font color="Olive" title="b2">s</font>,<font color="Olive" title="b3">n</font>) is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  holds <br/> <a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Olive" title="b2">s</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> (<font color="Olive" title="b2">s</font>,<font color="Olive" title="b3">n</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</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">S</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">s</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c2">A</font><br/>  for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st  <a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> (<font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">n</font>) is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  holds <br/> <a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Olive" title="b1">s</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> (<font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">n</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c2">A</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">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st  <a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> (<font color="Maroon" title="c3">s</font>,<font color="Olive" title="b1">n</font>) is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  holds <br/> <a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c3">s</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> (<font color="Maroon" title="c3">s</font>,<font color="Olive" title="b1">n</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</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"> (  <a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">n</font>) is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>  implies  <a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c3">s</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">n</font>) )</span><br/>







<span class="kw">assume </span><a NAME="E1:9"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
 <a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">n</font>) is  <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</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">  <a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c3">s</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">n</font>)</span><br/>

<a NAME="E2:9"/><span class="kw">then </span>
<font color="Maroon" title="c3">s</font> is  <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E3:9"/>
 <a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c3">s</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="circcmb3.html#D4" target="_self" onmouseover="rs('circcmb3/D4')" onmouseout="rh()">Def4</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"> verum</span><br/>


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