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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   non  <a href="xtuple_0.html#V1" title="XTUPLE_0:attr.1">pair</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K19" title="FACIRC_1:func.19">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"><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><br/>

<span class="kw">set </span><font color="Maroon" title="c4">S</font> =  <a href="facirc_1.html#K19" title="FACIRC_1:func.19">BitAdderWithOverflowStr</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">set </span><font color="Maroon" title="c5">S1</font> =  <a href="facirc_1.html#K8" title="FACIRC_1:func.8">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>);<br/>
<span class="kw">set </span><font color="Maroon" title="c6">S2</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/>
<a NAME="E1:121"/><span class="lab"><font color="Green" title="E67">A1</font></span>: 
(  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K8" title="FACIRC_1:func.8">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> <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> &amp;  <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="ref" href="facirc_1.html#T57" target="_self" onmouseover="rs('facirc_1/T57')" onmouseout="rh()">Th57</a>, <a class="ref" href="facirc_1.html#T75" target="_self" onmouseover="rs('facirc_1/T75')" onmouseout="rh()">Th75</a></span>;<br/>
<a NAME="E2:121"/>
(  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K8" title="FACIRC_1:func.8">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> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a> &amp;  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</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> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T58" target="_self" onmouseover="rs('facirc_1/T58')" onmouseout="rh()">Th58</a>, <a class="ref" href="facirc_1.html#T67" target="_self" onmouseover="rs('facirc_1/T67')" onmouseout="rh()">Th67</a></span>;<br/>
<span class="kw">hence </span> <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K19" title="FACIRC_1:func.19">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"><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> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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="#E1:121"><span class="lab"><font color="Green" title="E67">A1</font></span></a>, <a class="ref" href="facirc_1.html#T7" target="_self" onmouseover="rs('facirc_1/T7')" onmouseout="rh()">Th7</a></span>
<br/>.= 
<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>

;<br/> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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