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

<b>let </b><font color="Maroon">x</font> be  non <a href="facirc_1.html#V1">pair</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">b</font> be  non <a href="facirc_1.html#V1">pair</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">s</font> be   <a href="circuit1.html#NM3">State</a> of <span class="p1">(<span class="default"><a href="twoscomp.html#K41" target="_self">BitCompCirc</a> <font color="Maroon">x</font>,<font color="Maroon">b</font></span>)</span>;<br/>



<b>set </b><font color="Maroon">p</font> = <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">b</font></span><a href="facirc_1.html#K6">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">S</font> =  <a href="twoscomp.html#K40" target="_self">BitCompStr</a> <font color="Maroon">x</font>,<font color="Maroon">b</font>;<br/>
<a NAME="E1:59"/>
 <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K40" target="_self">BitCompStr</a> <font color="Maroon">x</font>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="twoscomp.html#D16" target="_self">Def16</a></i>;<br/>
<a NAME="E2:59"/><b>then </b><i><font color="Green">E70</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K40" target="_self">BitCompStr</a> <font color="Maroon">x</font>,<font color="Maroon">b</font></span>)</span> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K40" target="_self">BitCompStr</a> <font color="Maroon">x</font>,<font color="Maroon">b</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E3:59"/><i><font color="Green">E87</font></i>: 
 <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K40" target="_self">BitCompStr</a> <font color="Maroon">x</font>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="twoscomp.html#K40" target="_self">BitCompStr</a> <font color="Maroon">x</font>,<font color="Maroon">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="facirc_1.html#T37">FACIRC_1:37</a></i>;<br/>
<a NAME="E4:59"/><i><font color="Green">E88</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="twoscomp.html#K40" target="_self">BitCompStr</a> <font color="Maroon">x</font>,<font color="Maroon">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="circuit1.html#T4">CIRCUIT1:4</a></i>;<br/>
<a NAME="E5:59"/><i><font color="Green">E89</font></i>: 
( <font color="Maroon">x</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="twoscomp.html#K40" target="_self">BitCompStr</a> <font color="Maroon">x</font>,<font color="Maroon">b</font></span>)</span> &amp; <font color="Maroon">b</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="twoscomp.html#K40" target="_self">BitCompStr</a> <font color="Maroon">x</font>,<font color="Maroon">b</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="twoscomp.html#D12" target="_self">Def12</a></i>;<br/>
<a NAME="E6:59"/><i><font color="Green">E93</font></i>: 
<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">x</font>,<font color="Maroon">b</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K3" target="_self">and2a</a> </span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K40" target="_self">BitCompStr</a> <font color="Maroon">x</font>,<font color="Maroon">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="twoscomp.html#D15" target="_self">Def15</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K39" target="_self">IncrementOutput</a> <font color="Maroon">x</font>,<font color="Maroon">b</font></span>)</span> = 
<a href="twoscomp.html#K3" target="_self">and2a</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">b</font></span><a href="facirc_1.html#K6">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="twoscomp.html#D23" target="_self">Def23</a>, <a class="ref" href="twoscomp.html#D26" target="_self">Def26</a>, <a class="ref" href="facirc_1.html#T35">FACIRC_1:35</a></i>
<br/>.= 
<a href="twoscomp.html#K3" target="_self">and2a</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font></span>)</span></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#D24" target="_self">Def24</a>, <a class="ref" href="twoscomp.html#D25" target="_self">Def25</a>, <a class="ref" href="finseq_2.html#T145">FINSEQ_2:145</a></i>
;<br/>

<b>thus </b><a NAME="E8:59"/>
( <span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="twoscomp.html#D22" target="_self">Def22</a>, <a class="ref" href="circuit2.html#D5">CIRCUIT2:def 5</a></i>;<br/>


</div>
