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<b>let </b><font color="Maroon" title="c1">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon">F<sub>5</sub></font>() <a href="circcmb3.html#K9" title="CIRCCMB3:func.9">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K7" title="CIRCCMB3:func.7">1GateCircuit</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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">F<sub>5</sub></font>()  st <font color="Olive" title="b1">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>4</sub></font>() holds <br/>for <font color="Olive" title="b2">a1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()  st ( <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>() implies <font color="Olive" title="b2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Olive" title="b1">s'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>1</sub></font>() ) &amp; ( not <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>() implies <font color="Olive" title="b2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>1</sub></font>() ) holds <br/><span class="p1">(<span class="default"><a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K5" title="CIRCCMB3:func.5">Output</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b2">a1</font>)</span><br/><b>let </b><font color="Maroon" title="c2">s'</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon">F<sub>5</sub></font>(); <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>4</sub></font>() implies for <font color="Olive" title="b1">a1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()  st ( <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>() implies <font color="Olive" title="b1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c2">s'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>1</sub></font>() ) &amp; ( not <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>() implies <font color="Olive" title="b1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>1</sub></font>() ) holds <br/><span class="p1">(<span class="default"><a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K5" title="CIRCCMB3:func.5">Output</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">a1</font>) )</span><br/>



<b>assume </b><a NAME="E1:96_1"/><i><font color="Green" title="E53">A3</font></i>: 
<font color="Maroon" title="c2">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>4</sub></font>()
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()  st ( <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>() implies <font color="Olive" title="b1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c2">s'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>1</sub></font>() ) &amp; ( not <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>() implies <font color="Olive" title="b1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>1</sub></font>() ) holds <br/><span class="p1">(<span class="default"><a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K5" title="CIRCCMB3:func.5">Output</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">a1</font>)</span><br/>

<b>let </b><font color="Maroon" title="c3">a1</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>(); <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>() implies <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c2">s'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>1</sub></font>() ) &amp; ( not <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>() implies <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>1</sub></font>() ) implies <span class="p1">(<span class="default"><a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K5" title="CIRCCMB3:func.5">Output</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c3">a1</font>) )</span><br/>

<b>assume </b><a NAME="E2:96_1"/><i><font color="Green" title="E54">A4</font></i>: 
( ( <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>() implies <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c2">s'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>1</sub></font>() ) &amp; ( not <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>() implies <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>1</sub></font>() ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K5" title="CIRCCMB3:func.5">Output</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c3">a1</font>)</span><br/>

<b>set </b><font color="Maroon" title="c4">S</font> =  <a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>();<br/>
<a NAME="E3:96_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T55" title="FINSEQ_1:th.55">FINSEQ_1:55</a></i>;<br/>
<a NAME="E4:96_1"/><b>then </b><i><font color="Green" title="E55">A5</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span> &amp; <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="circcomb.html#T49" title="CIRCCOMB:th.49">CIRCCOMB:49</a>, <a class="ref" href="circcomb.html#D6" title="CIRCCOMB:def.6">CIRCCOMB:def 6</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E5:96_1"/><b>then </b>
( <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>4</sub></font>() <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span> )
 
<b>by </b><i><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></i>;<br/>
<a NAME="E6:96_1"/><b>then </b><i><font color="Green" title="E56">A6</font></i>: 
<font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E7:96_1"/>
 <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="circcmb3.html#K5" title="CIRCCMB3:func.5">Output</a> <span class="p3">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p4"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="circcmb3.html#T17" target="_self" title="CIRCCMB3:th.17">Th17</a></i>;<br/>
<a NAME="E8:96_1"/><b>then </b><i><font color="Green" title="E57">A7</font></i>: 
 <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon">F<sub>4</sub></font>() <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span>
 
<b>by </b><i><a class="txt" href="circcmb3.html#E2:96"><i><font color="Green" title="E52">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></i>;<br/>
<a NAME="E9:96_1"/>
<font color="Maroon">F<sub>5</sub></font>() <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a>  <a href="circcmb3.html#K7" title="CIRCCMB3:func.7">1GateCircuit</a> <span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()
 
<b>by </b><i><a class="ref" href="circcmb3.html#T30" target="_self" title="CIRCCMB3:th.30">Th30</a></i>;<br/>
<a NAME="E10:96_1"/><b>then </b>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon">F<sub>5</sub></font>() <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="circcmb3.html#K7" title="CIRCCMB3:func.7">1GateCircuit</a> <span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span>
 
<b>by </b><i><a class="ref" href="circcomb.html#D3" title="CIRCCOMB:def.3">CIRCCOMB:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">s1</font> = <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c1">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c2">s'</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span> as   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="circcmb3.html#K7" title="CIRCCMB3:func.7">1GateCircuit</a> <span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span> <b>by </b><i><a class="ref" href="circcomb.html#T33" title="CIRCCOMB:th.33">CIRCCOMB:33</a></i>;<br/>
<a NAME="E12:96_1"/><i><font color="Green" title="E58">A8</font></i>: 
( <font color="Maroon" title="c1">s</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> &amp; <font color="Maroon" title="c2">s'</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> &amp; <font color="Maroon" title="c5">s1</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> )
 
<b>by </b><i><a class="ref" href="circcmb3.html#D2" target="_self" title="CIRCCMB3:def.2">Def2</a></i>;<br/>
<a NAME="E13:96_1"/>
<font color="Maroon">F<sub>4</sub></font>() <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a>  <a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()
 
<b>by </b><i><a class="ref" href="circcomb.html#T55" title="CIRCCOMB:th.55">CIRCCOMB:55</a></i>;<br/>
<a NAME="E14:96_1"/><b>then </b><i><font color="Green" title="E59">A9</font></i>: 
 <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p3">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p4"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="circcmb3.html#E8:96_1"><i><font color="Green" title="E57">A7</font></i></a>, <a class="ref" href="facirc_1.html#T4" title="FACIRC_1:th.4">FACIRC_1:4</a></i>;<br/>
<a NAME="E15:96_1"/>
( <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>() or <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> )
 
<b>by </b><i><a class="txt" href="circcmb3.html#E4:96_1"><i><font color="Green" title="E55">A5</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E16:96_1"/><b>then </b><i><font color="Green" title="E60">A10</font></i>: 
( <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>() or <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="circcmb3.html#E14:96_1"><i><font color="Green" title="E59">A9</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c1">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c2">s'</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>4</sub></font>() = 
 <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c2">s'</font>,<span class="p1">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c2">s'</font></span>)</span>
<b>by </b><i><a class="txt" href="circcmb3.html#E1:96_1"><i><font color="Green" title="E53">A3</font></i></a>, <a class="txt" href="circcmb3.html#E8:96_1"><i><font color="Green" title="E57">A7</font></i></a>, <a class="ref" href="circcmb3.html#T30" target="_self" title="CIRCCMB3:th.30">Th30</a>, <a class="ref" href="circcmb2.html#T14" title="CIRCCMB2:th.14">CIRCCMB2:14</a></i>
<br/>.= 
 <a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c2">s'</font>
<b>by </b><i><a class="txt" href="circcmb3.html#E12:96_1"><i><font color="Green" title="E58">A8</font></i></a>, <a class="ref" href="circcmb3.html#T2" target="_self" title="CIRCCMB3:th.2">Th2</a></i>
;<br/>
<a NAME="E18:96_1"/><b>then </b><i><font color="Green" title="E61">A11</font></i>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c1">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c2">s'</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>1</sub></font>()
 
<b>by </b><i><a class="txt" href="circcmb3.html#E2:96_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="txt" href="circcmb3.html#E16:96_1"><i><font color="Green" title="E60">A10</font></i></a>, <a class="ref" href="circcmb3.html#T1" target="_self" title="CIRCCMB3:th.1">Th1</a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/>
<a NAME="E19:96_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c1">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c2">s'</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="circuit1.html#T4" title="CIRCUIT1:th.4">CIRCUIT1:4</a></i>;<br/>
<a NAME="E20:96_1"/><b>then </b><i><font color="Green" title="E62">A12</font></i>: 
<span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c1">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c2">s'</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">a1</font></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="circcmb3.html#E6:96_1"><i><font color="Green" title="E56">A6</font></i></a>, <a class="txt" href="circcmb3.html#E18:96_1"><i><font color="Green" title="E61">A11</font></i></a>, <a class="ref" href="circcmb3.html#T36" target="_self" title="CIRCCMB3:th.36">Th36</a></i>;<br/>
<a NAME="E21:96_1"/><i><font color="Green" title="E63">A13</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circcmb3.html#K5" title="CIRCCMB3:func.5">Output</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span>
 
<b>by </b><i><a class="ref" href="circcmb3.html#T16" target="_self" title="CIRCCMB3:th.16">Th16</a></i>;<br/>
<a NAME="E22:96_1"/>
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="circcomb.html#D6" title="CIRCCOMB:def.6">CIRCCOMB:def 6</a></i>;<br/>
<a NAME="E23:96_1"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon">F<sub>4</sub></font>() <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<b>by </b><i><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">g</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as   <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<i><font color="Green" title="E64">A14</font></i>:  <a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c6">g</font> = 
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">g</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D7" title="MSUALG_1:def.7">MSUALG_1:def 7</a></i>
<br/>.= 
<font color="Maroon" title="c6">g</font>
<b>by </b><i><a class="ref" href="circcomb.html#T52" title="CIRCCOMB:th.52">CIRCCOMB:52</a></i>
;<br/>
<a NAME="E26:96_1"/>
<font color="Maroon" title="c6">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default">the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p3">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p4">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p5"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
<b>by </b><i><a class="ref" href="circcomb.html#D8" title="CIRCCOMB:def.8">CIRCCOMB:def 8</a></i>;<br/>
<b>then </b><i><font color="Green" title="E65">A15</font></i>: <span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span> = 
the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">g</font>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>
<br/>.= 
 <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c6">g</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D6" title="MSUALG_1:def.6">MSUALG_1:def 6</a></i>
;<br/>
<a NAME="E28:96_1"/><i><font color="Green" title="E66">A16</font></i>: 
<font color="Maroon" title="c6">g</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>6</sub></font>()
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<a NAME="E29:96_1"/>
 <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c1">s</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c2">s'</font></span>)</span>
 
<b>by </b><i><a class="txt" href="circcmb3.html#E2:96"><i><font color="Green" title="E52">A2</font></i></a>, <a class="txt" href="circcmb3.html#E1:96_1"><i><font color="Green" title="E53">A3</font></i></a>, <a class="ref" href="circcmb3.html#T52" target="_self" title="CIRCCMB3:th.52">Th52</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K5" title="CIRCCMB3:func.5">Output</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c1">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c2">s'</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K5" title="CIRCCMB3:func.5">Output</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="circcmb3.html#E12:96_1"><i><font color="Green" title="E58">A8</font></i></a>, <a class="ref" href="circcmb3.html#T5" target="_self" title="CIRCCMB3:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <span class="p2">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c1">s</font>,<span class="p3">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c2">s'</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">g</font>
<b>by </b><i><a class="txt" href="circcmb3.html#E21:96_1"><i><font color="Green" title="E63">A13</font></i></a>, <a class="ref" href="facirc_1.html#T12" title="FACIRC_1:th.12">FACIRC_1:12</a></i>
<br/>.= 
<font color="Maroon">F<sub>6</sub></font>() <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c1">s</font>,<span class="p3">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c2">s'</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="circcmb3.html#E25:96_1"><i><font color="Green" title="E64">A14</font></i></a>, <a class="txt" href="circcmb3.html#E27:96_1"><i><font color="Green" title="E65">A15</font></i></a>, <a class="txt" href="circcmb3.html#E28:96_1"><i><font color="Green" title="E66">A16</font></i></a>, <a class="ref" href="facirc_1.html#T34" title="FACIRC_1:th.34">FACIRC_1:34</a></i>
<br/>.= 
<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c3">a1</font>)
<b>by </b><i><a class="txt" href="circcmb3.html#E1:96"><i><font color="Green" title="E51">A1</font></i></a>, <a class="txt" href="circcmb3.html#E20:96_1"><i><font color="Green" title="E62">A12</font></i></a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
