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<b>let </b><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> ;<br/>

<a NAME="E1:36"/>
 <a href="facirc_1.html#K12" title="FACIRC_1:func.12">2GatesCircStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font>,<a href="facirc_1.html#K1" title="FACIRC_1:func.1">'xor'</a>  <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a>  <a href="facirc_1.html#K19" title="FACIRC_1:func.19">MajorityStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font>
 
<b>by </b><i><a class="ref" href="circcomb.html#T55" title="CIRCCOMB:th.55">CIRCCOMB:55</a></i>;<br/>
<b>then </b> <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K23" title="FACIRC_1:func.23">BitAdderWithOverflowStr</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="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p2">(<span class="default"><a href="facirc_1.html#K12" title="FACIRC_1:func.12">2GatesCircStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font>,<a href="facirc_1.html#K1" title="FACIRC_1:func.1">'xor'</a> </span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p2">(<span class="default"><a href="facirc_1.html#K19" title="FACIRC_1:func.19">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>)</span>
<b>by </b><i><a class="ref" href="circcomb.html#T15" title="CIRCCOMB:th.15">CIRCCOMB:15</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</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#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="facirc_1.html#K1" title="FACIRC_1:func.1">'xor'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><a href="facirc_1.html#K13" title="FACIRC_1:func.13">2GatesCircOutput</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font>,<a href="facirc_1.html#K1" title="FACIRC_1:func.1">'xor'</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p2">(<span class="default"><a href="facirc_1.html#K19" title="FACIRC_1:func.19">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>)</span>
<b>by </b><i><a class="ref" href="facirc_1.html#T56" title="FACIRC_1:th.56">FACIRC_1:56</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</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#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="facirc_1.html#K1" title="FACIRC_1:func.1">'xor'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><a href="facirc_1.html#K13" title="FACIRC_1:func.13">2GatesCircOutput</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font>,<a href="facirc_1.html#K1" title="FACIRC_1:func.1">'xor'</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&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="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&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="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&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><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="facirc_1.html#K21" title="FACIRC_1:func.21">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></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="facirc_2.html#T20" target="_self" title="FACIRC_2:th.20">Th20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="facirc_1.html#K1" title="FACIRC_1:func.1">'xor'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3">(<span class="default"><a href="facirc_1.html#K13" title="FACIRC_1:func.13">2GatesCircOutput</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font>,<a href="facirc_1.html#K1" title="FACIRC_1:func.1">'xor'</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&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="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&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="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&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><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</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">(<span class="default"><a href="facirc_1.html#K21" title="FACIRC_1:func.21">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></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>
;<br/>
<b>hence </b><a NAME="E3:36"/>
 <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K23" title="FACIRC_1:func.23">BitAdderWithOverflowStr</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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="facirc_1.html#K1" title="FACIRC_1:func.1">'xor'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3">(<span class="default"><a href="facirc_1.html#K13" title="FACIRC_1:func.13">2GatesCircOutput</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font>,<a href="facirc_1.html#K1" title="FACIRC_1:func.1">'xor'</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&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="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&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="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&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><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</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">(<span class="default"><a href="facirc_1.html#K21" title="FACIRC_1:func.21">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></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>


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