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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<a NAME="E1:19"/>
( <span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/>
<b>hence </b><a NAME="E2:19"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><a href="facirc_2.html#K3" target="_self">&lt;*&gt;</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default">0 <a href="finseq_2.html#K4">-tuples_on</a> <a href="circcomb.html#K10">BOOLEAN</a> </span>)</span> <a href="circcomb.html#K5">--&gt;</a> <a href="margrel1.html#K7">FALSE</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> holds <br/>( 1 <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span>,<span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <a href="facirc_2.html#K3" target="_self">&lt;*&gt;</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default">0 <a href="finseq_2.html#K4">-tuples_on</a> <a href="circcomb.html#K10">BOOLEAN</a> </span>)</span> <a href="circcomb.html#K5">--&gt;</a> <a href="margrel1.html#K7">FALSE</a> </span>)</span></span>)</span> <a href="circcomb.html#K3">+*</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K23">BitAdderWithOverflowStr</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> &amp; 1 <a href="facirc_2.html#K5" target="_self">-BitAdderCirc</a> <span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span>,<span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="circcomb.html#K9">1GateCircuit</a> <a href="facirc_2.html#K3" target="_self">&lt;*&gt;</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default">0 <a href="finseq_2.html#K4">-tuples_on</a> <a href="circcomb.html#K10">BOOLEAN</a> </span>)</span> <a href="circcomb.html#K5">--&gt;</a> <a href="margrel1.html#K7">FALSE</a> </span>)</span></span>)</span> <a href="circcomb.html#K4">+*</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K24">BitAdderWithOverflowCirc</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> &amp; 1 <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span>,<span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="facirc_1.html#K21">MajorityOutput</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="facirc_2.html#T9" target="_self">Th9</a></i>;<br/>


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