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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">c</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> implies for <font color="Olive" title="b1">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="facirc_1.html#K18" title="FACIRC_1:func.18">MajorityCirc</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span><br/> for <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">a3</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K8" title="CIRCCOMB:func.8">BOOLEAN</a>   st <font color="Olive" title="b2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Olive" title="b3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">y</font> &amp; <font color="Olive" title="b4">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">c</font> holds <br/>( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,2</span>)</span> <a href="facirc_1.html#K11" title="FACIRC_1:func.11">.</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K17" title="FACIRC_1:func.17">MajorityOutput</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b3">a2</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">a2</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b4">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b2">a1</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b3">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a2</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b4">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b2">a1</font> ) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:47"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E2:47"/><span class="lab"><font color="Green" title="E30">A2</font></span>: 
<font color="Maroon" title="c2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E3:47"/><span class="lab"><font color="Green" title="E31">A3</font></span>: 
<font color="Maroon" title="c3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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 <span class="p1">(<span class="default"><a href="facirc_1.html#K18" title="FACIRC_1:func.18">MajorityCirc</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span><br/> for <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">a3</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K8" title="CIRCCOMB:func.8">BOOLEAN</a>   st <font color="Olive" title="b2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Olive" title="b3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">y</font> &amp; <font color="Olive" title="b4">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">c</font> holds <br/>( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,2</span>)</span> <a href="facirc_1.html#K11" title="FACIRC_1:func.11">.</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K17" title="FACIRC_1:func.17">MajorityOutput</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b3">a2</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">a2</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b4">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b2">a1</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b3">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a2</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b4">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Olive" title="b1">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b2">a1</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="facirc_1.html#K18" title="FACIRC_1:func.18">MajorityCirc</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">a3</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K8" title="CIRCCOMB:func.8">BOOLEAN</a>   st <font color="Olive" title="b1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Olive" title="b2">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">y</font> &amp; <font color="Olive" title="b3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">c</font> holds <br/>( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="facirc_1.html#K11" title="FACIRC_1:func.11">.</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K17" title="FACIRC_1:func.17">MajorityOutput</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b2">a2</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">a2</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b3">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b1">a1</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b2">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a2</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b3">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b1">a1</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">a1</font>, <font color="Maroon" title="c6">a2</font>, <font color="Maroon" title="c7">a3</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K8" title="CIRCCOMB:func.8">BOOLEAN</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">y</font> &amp; <font color="Maroon" title="c7">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">c</font> implies ( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="facirc_1.html#K11" title="FACIRC_1:func.11">.</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K17" title="FACIRC_1:func.17">MajorityOutput</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c6">a2</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">a2</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c7">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c5">a1</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c6">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c7">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c5">a1</font> ) )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E4:47"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
<font color="Maroon" title="c5">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font>
 <span class="kw">and </span><br/><a NAME="E5:47"/><span class="lab"><font color="Green" title="E33">A5</font></span>: 
<font color="Maroon" title="c6">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">y</font>
 <span class="kw">and </span><br/><a NAME="E6:47"/><span class="lab"><font color="Green" title="E34">A6</font></span>: 
<font color="Maroon" title="c7">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="facirc_1.html#K11" title="FACIRC_1:func.11">.</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K17" title="FACIRC_1:func.17">MajorityOutput</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c6">a2</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">a2</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c7">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c5">a1</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c6">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c7">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c5">a1</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">xy</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">yc</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">cx</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">S</font> =  <a href="facirc_1.html#K15" title="FACIRC_1:func.15">MajorityStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">x9</font> = <font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c13">y9</font> = <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c14">c9</font> = <font color="Maroon" title="c3">c</font> as   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <span class="p1">(<span class="default"><a href="facirc_1.html#K15" title="FACIRC_1:func.15">MajorityStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T72" title="FACIRC_1:th.72">FACIRC_1:72</a></span>;<br/>
<a NAME="E8:47"/><span class="lab"><font color="Green" title="E35">A7</font></span>: 
 <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K15" title="FACIRC_1:func.15">MajorityStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E2:47"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E3:47"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="ref" href="facirc_2.html#T21" target="_self" title="FACIRC_2:th.21">Th21</a></span>;<br/>
<a NAME="E9:47"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A8</font></span>: 
<font color="Maroon" title="c1">x</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"><a href="facirc_1.html#K15" title="FACIRC_1:func.15">MajorityStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>;<br/>
<a NAME="E10:47"/><span class="lab"><font color="Green" title="E37">A9</font></span>: 
<font color="Maroon" title="c2">y</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"><a href="facirc_1.html#K15" title="FACIRC_1:func.15">MajorityStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:47"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>;<br/>
<a NAME="E11:47"/><span class="lab"><font color="Green" title="E38">A10</font></span>: 
<font color="Maroon" title="c3">c</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"><a href="facirc_1.html#K15" title="FACIRC_1:func.15">MajorityStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:47"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>;<br/>
<a NAME="E12:47"/><span class="lab"><font color="Green" title="E39">A11</font></span>: 
<span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="facirc_1.html#K11" title="FACIRC_1:func.11">.</a> <font color="Maroon" title="c12">x9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:47"><span class="lab"><font color="Green" title="E36">A8</font></span></a>, <a class="ref" href="circuit2.html#D5" title="CIRCUIT2:def.5">CIRCUIT2:def 5</a></span>;<br/>
<a NAME="E13:47"/><span class="lab"><font color="Green" title="E40">A12</font></span>: 
<span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="facirc_1.html#K11" title="FACIRC_1:func.11">.</a> <font color="Maroon" title="c13">y9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:47"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="circuit2.html#D5" title="CIRCUIT2:def.5">CIRCUIT2:def 5</a></span>;<br/>
<a NAME="E14:47"/><span class="lab"><font color="Green" title="E41">A13</font></span>: 
<span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="facirc_1.html#K11" title="FACIRC_1:func.11">.</a> <font color="Maroon" title="c14">c9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:47"><span class="lab"><font color="Green" title="E38">A10</font></span></a>, <a class="ref" href="circuit2.html#D5" title="CIRCUIT2:def.5">CIRCUIT2:def 5</a></span>;<br/>
<a NAME="E15:47"/><span class="lab"><font color="Green" title="E42">A14</font></span>: 
 <a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2 <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c4">s</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T15" title="FACIRC_1:th.15">FACIRC_1:15</a></span>;<br/>
<a NAME="E16:47"/><span class="lab"><font color="Green" title="E43">A15</font></span>: 
<span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c6">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E5:47"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E6:47"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="facirc_2.html#E37"><span class="lab"><font color="Green" title="E26">Lm3</font></span></a></span>;<br/>
<a NAME="E17:47"/><span class="lab"><font color="Green" title="E44">A16</font></span>: 
<span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c7">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E5:47"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E6:47"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="facirc_2.html#E37"><span class="lab"><font color="Green" title="E26">Lm3</font></span></a></span>;<br/>
<a NAME="E18:47"/>
<span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c5">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E5:47"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E6:47"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="facirc_2.html#E37"><span class="lab"><font color="Green" title="E26">Lm3</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E19:47"/>
<span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="facirc_1.html#K11" title="FACIRC_1:func.11">.</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K17" title="FACIRC_1:func.17">MajorityOutput</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c6">a2</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">a2</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c7">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c5">a1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:47"><span class="lab"><font color="Green" title="E42">A14</font></span></a>, <a class="txt" href="#E16:47"><span class="lab"><font color="Green" title="E43">A15</font></span></a>, <a class="txt" href="#E17:47"><span class="lab"><font color="Green" title="E44">A16</font></span></a>, <a class="ref" href="facirc_2.html#T29" target="_self" title="FACIRC_2:th.29">Th29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c6">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c7">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c5">a1</font> )</span><br/>

<span class="kw">thus </span><a NAME="E20:47"/>
( <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c6">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c7">a3</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">Following</a> <font color="Maroon" title="c4">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c5">a1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E5:47"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E6:47"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E12:47"><span class="lab"><font color="Green" title="E39">A11</font></span></a>, <a class="txt" href="#E13:47"><span class="lab"><font color="Green" title="E40">A12</font></span></a>, <a class="txt" href="#E14:47"><span class="lab"><font color="Green" title="E41">A13</font></span></a>, <a class="txt" href="#E15:47"><span class="lab"><font color="Green" title="E42">A14</font></span></a>, <a class="txt" href="facirc_2.html#E37"><span class="lab"><font color="Green" title="E26">Lm3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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