<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon">c<sub>1</sub></font> =  <a href="twoscomp.html#K14">xor2</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="twoscomp.html#K2">and2</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="twoscomp.html#K2">and2</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="twoscomp.html#K2">and2</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="twoscomp.html#K25">or3</a> ;<br/>
<b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>9</sub></font> = <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>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> = <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>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> = <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>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span>,<span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span>,<span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span></span><a href="facirc_1.html#K7">*&gt;</a></span>,<a href="twoscomp.html#K25">or3</a> </span><a href="tarski.html#K4">]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> =  <a href="gfacirc1.html#K10" target="_self">GFA0AdderStr</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>14</sub></font> =  <a href="gfacirc1.html#K7" target="_self">GFA0CarryStr</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>;<br/>
<a NAME="E1:56"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K10" target="_self">GFA0AdderStr</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K10" target="_self">GFA0AdderStr</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K10" target="_self">GFA0AdderStr</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <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>6</sub></font>,<font color="Maroon">c<sub>7</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#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K10" target="_self">GFA0AdderStr</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <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"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</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>,<font color="Maroon">c<sub>8</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#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K10" target="_self">GFA0AdderStr</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="facirc_1.html#T60">FACIRC_1:60</a>, <a class="ref" href="facirc_1.html#T61">FACIRC_1:61</a></i>;<br/>
<a NAME="E2:56"/>
( <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>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K7" target="_self">GFA0CarryStr</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <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>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K7" target="_self">GFA0CarryStr</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <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>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K7" target="_self">GFA0CarryStr</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span>,<span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span>,<span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span></span><a href="facirc_1.html#K7">*&gt;</a></span>,<a href="twoscomp.html#K25">or3</a> </span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K7" target="_self">GFA0CarryStr</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gfacirc1.html#T19" target="_self">Th19</a></i>;<br/>
<b>hence </b><a NAME="E3:56"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" target="_self">BitGFA0Str</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" target="_self">BitGFA0Str</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" target="_self">BitGFA0Str</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <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>6</sub></font>,<font color="Maroon">c<sub>7</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#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" target="_self">BitGFA0Str</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <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"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</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>,<font color="Maroon">c<sub>8</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#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" target="_self">BitGFA0Str</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <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>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" target="_self">BitGFA0Str</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <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>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" target="_self">BitGFA0Str</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <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>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" target="_self">BitGFA0Str</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span>,<span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span>,<span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span></span><a href="facirc_1.html#K7">*&gt;</a></span>,<a href="twoscomp.html#K25">or3</a> </span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K13" target="_self">BitGFA0Str</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="gfacirc1.html#E1:56"><i><font color="Green">E36</font></i></a>, <a class="ref" href="facirc_1.html#T20">FACIRC_1:20</a></i>;<br/>


</div>
