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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be  <a href="group_1.html#V6">finite</a>  <a href="circcmb3.html#M1" target="_self">Signature</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="circcmb3.html#M2" target="_self">Circuit</a> of <font color="Maroon">X</font>,<font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">X</font>,<font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="circcomb.html#M1">FinSeqLen</a> of <font color="Maroon">n</font>;<br/>











<b>assume </b><a NAME="E1:95"/><i><font color="Green">E34</font></i>: 
not  <a href="circcmb3.html#K5" target="_self">Output</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">S</font>
 ;<br/>

<b>let </b><font color="Maroon">s</font> be   <a href="circuit1.html#NM3">State</a> of <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="circcmb3.html#K9" target="_self">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K7" target="_self">1GateCircuit</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span></span>)</span>;<br/><b>let </b><font color="Maroon">s'</font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">A</font>;<br/>



<b>assume </b><a NAME="E2:95"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">s'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 ;<br/>

<a NAME="E3:95"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">A</font> <a href="circcomb.html#R2">tolerates</a>  <a href="circcmb3.html#K7" target="_self">1GateCircuit</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="circcmb3.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E4:95"/><b>then </b>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="circcmb3.html#K7" target="_self">1GateCircuit</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="circcomb.html#D3">CIRCCOMB:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">s1</font> = <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"><a href="circcmb3.html#K2" target="_self">stabilization-time</a> <font color="Maroon">s'</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> as   <a href="circuit1.html#NM3">State</a> of <span class="p1">(<span class="default"><a href="circcmb3.html#K7" target="_self">1GateCircuit</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <b>by </b><i><a class="ref" href="circcomb.html#T33">CIRCCOMB:33</a></i>;<br/>
<a NAME="E6:95"/><i><font color="Green">E38</font></i>: 
 <a href="circcmb3.html#K2" target="_self">stabilization-time</a> <font color="Maroon">s1</font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 
<b>by </b><i/>;<br/>
<a NAME="E7:95"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">s'</font> is <a href="circcmb3.html#V1" target="_self">stabilizing</a> &amp; <font color="Maroon">s1</font> is <a href="circcmb3.html#V1" target="_self">stabilizing</a> )
 
<b>by </b><i/>;<br/>
<a NAME="E8:95"/>
 <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="circcmb3.html#K5" target="_self">Output</a> <span class="p3">(<span class="default"><a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E9:95"/><b>then </b>
 <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">S</font> <a href="xboole_0.html#R1">misses</a>  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="circcmb3.html#T2" target="_self">Th2</a>, <a class="ref" href="zfmisc_1.html#T56">ZFMISC_1:56</a></i>;<br/>
<a NAME="E10:95"/><b>then </b>
 <a href="circcmb3.html#K2" target="_self">stabilization-time</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K2" target="_self">stabilization-time</a> <font color="Maroon">s'</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K2" target="_self">stabilization-time</a> <font color="Maroon">s1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="circcmb3.html#T4" target="_self">Th4</a>, <a class="ref" href="circcmb3.html#T5" target="_self">Th5</a>, , </i>;<br/>
<b>hence </b><a NAME="E11:95"/>
 <a href="circcmb3.html#K2" target="_self">stabilization-time</a> <font color="Maroon">s</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K2" target="_self">stabilization-time</a> <font color="Maroon">s'</font></span>)</span>
 <b>by </b><i><a class="ref" href="circcmb3.html#T8" target="_self">Th8</a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>


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