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<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>let </b><font color="Maroon">a1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> , <font color="Maroon">a2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> ;<br/>





<b>assume </b><a NAME="E1:60"/><i><font color="Green">E70</font></i>: 
( <font color="Maroon">a1</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; <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> )
 ;<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"><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#D21" target="_self">Def21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">a1</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">a2</font>
<b>by </b><i><a class="ref" href="twoscomp.html#D23" target="_self">Def23</a>, </i>
;<br/>

<b>thus </b><a NAME="E3:60"/>
( <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">a1</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">a2</font> )
 <b>by </b><i><a class="ref" href="twoscomp.html#D23" target="_self">Def23</a>, <a class="ref" href="twoscomp.html#D21" target="_self">Def21</a></i>;<br/>


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