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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> = <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>;<br/>
<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="circcomb.html#M1">FinSeqLen</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span>;<br/>
<b>consider </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> being    <a href="pboole.html#M1">ManySortedSet</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E2:21"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="facirc_2.html#K5" target="_self">-BitAdderCirc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>and </b><br/><a NAME="E3:21"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a>  <a href="circcomb.html#K7">1GateCircStr</a> <a href="facirc_2.html#K3" target="_self">&lt;*&gt;</a> ,<span class="p1">(<span class="default"><span class="p2">(<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> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a>  <a href="circcomb.html#K9">1GateCircuit</a> <a href="facirc_2.html#K3" target="_self">&lt;*&gt;</a> ,<span class="p1">(<span class="default"><span class="p2">(<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> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> 0 <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> )
 <b>and </b><br/><a NAME="E4:21"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>2</sub></font> being non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> <br/>for <font color="Olive">b<sub>3</sub></font> being <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Olive">b<sub>2</sub></font><br/>for <font color="Olive">b<sub>4</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> holds <br/>( <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="circcomb.html#K3">+*</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K23">BitAdderWithOverflowStr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p4"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p4"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<font color="Olive">b<sub>4</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="circcomb.html#K4">+*</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K24">BitAdderWithOverflowCirc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p4"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p4"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<font color="Olive">b<sub>4</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="facirc_1.html#K21">MajorityOutput</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p3"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p3"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<font color="Olive">b<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="facirc_2.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E5:21"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="facirc_2.html#K5" target="_self">-BitAdderCirc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> )
 
<b>by </b><i><a class="txt" href="facirc_2.html#E3:21"><i><font color="Green">E12</font></i></a>, <a class="txt" href="facirc_2.html#E4:21"><i><font color="Green">E13</font></i></a>, <a class="ref" href="facirc_2.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E6:21"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="circcomb.html#D12">CIRCCOMB:def 12</a></i>;<br/>
<a NAME="E7:21"/><b>then </b><i><font color="Green">E15</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>;<br/>
<a NAME="E8:21"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <a href="facirc_2.html#K3" target="_self">&lt;*&gt;</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <a href="facirc_2.html#K3" target="_self">&lt;*&gt;</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/>
<a NAME="E9:21"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="facirc_2.html#K5" target="_self">-BitAdderCirc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="facirc_2.html#K5" target="_self">-BitAdderCirc</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="facirc_2.html#T11" target="_self">Th11</a></i>;<br/>
<b>hence </b><a NAME="E10:21"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></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>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="facirc_2.html#K5" target="_self">-BitAdderCirc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="facirc_2.html#K5" target="_self">-BitAdderCirc</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></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>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="facirc_1.html#K8">^</a> <span class="p2"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="facirc_1.html#K21">MajorityOutput</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="facirc_2.html#E2:21"><i><font color="Green">E11</font></i></a>, <a class="txt" href="facirc_2.html#E4:21"><i><font color="Green">E13</font></i></a>, <a class="txt" href="facirc_2.html#E5:21"><i><font color="Green">E14</font></i></a>, <a class="txt" href="facirc_2.html#E7:21"><i><font color="Green">E15</font></i></a></i>;<br/>


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