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<b>set </b><font color="Maroon">c<sub>1</sub></font> =  <a href="twoscomp.html#K14">xor2</a> ;<br/>
<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:176"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K14">xor2</a> </span><a href="tarski.html#K4">]</a></span>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="gfacirc1.html#K47" target="_self">GFA3AdderCirc</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="gfacirc1.html#K11" target="_self">GFA0AdderCirc</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="gfacirc1.html#K48" target="_self">GFA3AdderOutput</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="gfacirc1.html#K12" target="_self">GFA0AdderOutput</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<a NAME="E2:176"/>
(  <a href="gfacirc1.html#K47" target="_self">GFA3AdderCirc</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="gfacirc1.html#K11" target="_self">GFA0AdderCirc</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gfacirc1.html#K48" target="_self">GFA3AdderOutput</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="gfacirc1.html#K12" target="_self">GFA0AdderOutput</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
;<br/>
<b>hence </b><a NAME="E3:176"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="circuit1.html#NM3">State</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K47" target="_self">GFA3AdderCirc</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span><br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a>  st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> holds <br/>( <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Olive">b<sub>1</sub></font>,2</span>)</span> <a href="twoscomp.html#K1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K48" target="_self">GFA3AdderOutput</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="binarith.html#K4">'xor'</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="binarith.html#K4">'xor'</a> <font color="Olive">b<sub>4</sub></font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Olive">b<sub>1</sub></font>,2</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K14">xor2</a> </span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="binarith.html#K4">'xor'</a> <font color="Olive">b<sub>3</sub></font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Olive">b<sub>1</sub></font>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Olive">b<sub>1</sub></font>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Olive">b<sub>1</sub></font>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="gfacirc1.html#E1:176"><i><font color="Green">E99</font></i></a>, <a class="ref" href="gfacirc1.html#T37" target="_self">Th37</a></i>;<br/>


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