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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<a NAME="E1:19"/>
( <span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c1">a</font></span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> &amp; <span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></i>;<br/>
<b>hence </b><a NAME="E2:19"/>
for <font color="Olive" title="b1">c</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">c</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"><a href="facirc_2.html#K3" title="FACIRC_2:func.3">&lt;*&gt;</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default">0 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> </span>)</span> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">--&gt;</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/>( 1 <a href="facirc_2.html#K4" title="FACIRC_2:func.4">-BitAdderStr</a> <span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c1">a</font></span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c2">b</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">(<span class="default"><a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircStr</a> <a href="facirc_2.html#K3" title="FACIRC_2:func.3">&lt;*&gt;</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default">0 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> </span>)</span> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">--&gt;</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> </span>)</span></span>)</span> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</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">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">c</font></span>)</span> &amp; 1 <a href="facirc_2.html#K5" title="FACIRC_2:func.5">-BitAdderCirc</a> <span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c1">a</font></span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c2">b</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">(<span class="default"><a href="circcomb.html#K9" title="CIRCCOMB:func.9">1GateCircuit</a> <a href="facirc_2.html#K3" title="FACIRC_2:func.3">&lt;*&gt;</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default">0 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> </span>)</span> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">--&gt;</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> </span>)</span></span>)</span> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K24" title="FACIRC_1:func.24">BitAdderWithOverflowCirc</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">c</font></span>)</span> &amp; 1 <a href="facirc_2.html#K6" title="FACIRC_2:func.6">-BitMajorityOutput</a> <span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c1">a</font></span><a href="facirc_1.html#K5" title="FACIRC_1:func.5">*&gt;</a></span>,<span class="p1"><a href="facirc_1.html#K5" title="FACIRC_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c2">b</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>  <a href="facirc_1.html#K21" title="FACIRC_1:func.21">MajorityOutput</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">c</font> )
 <b>by </b><i><a class="ref" href="facirc_2.html#T9" target="_self" title="FACIRC_2:th.9">Th9</a></i>;<br/>


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