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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">b</font> be  non <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="twoscomp.html#K35" title="TWOSCOMP:func.35">CompCirc</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span>;<br/>



<b>set </b><font color="Maroon" title="c4">p</font> = <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c5">S</font> =  <a href="twoscomp.html#K34" title="TWOSCOMP:func.34">CompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font>;<br/>
<a NAME="E1:53"/>
 <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K34" title="TWOSCOMP:func.34">CompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="facirc_1.html#T40" title="FACIRC_1:th.40">FACIRC_1:40</a></i>;<br/>
<a NAME="E2:53"/><b>then </b><i><font color="Green" title="E42">A1</font></i>: 
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K34" title="TWOSCOMP:func.34">CompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span> &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K34" title="TWOSCOMP:func.34">CompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E3:53"/><i><font color="Green" title="E43">A2</font></i>: 
 <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K34" title="TWOSCOMP:func.34">CompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="twoscomp.html#K34" title="TWOSCOMP:func.34">CompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="facirc_1.html#T37" title="FACIRC_1:th.37">FACIRC_1:37</a></i>;<br/>
<a NAME="E4:53"/><i><font color="Green" title="E44">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="twoscomp.html#K34" title="TWOSCOMP:func.34">CompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="circuit1.html#T4" title="CIRCUIT1:th.4">CIRCUIT1:4</a></i>;<br/>
<a NAME="E5:53"/><i><font color="Green" title="E45">A4</font></i>: 
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="twoscomp.html#K34" title="TWOSCOMP:func.34">CompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span> &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="twoscomp.html#K34" title="TWOSCOMP:func.34">CompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="facirc_1.html#T43" title="FACIRC_1:th.43">FACIRC_1:43</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K36" title="TWOSCOMP:func.36">CompOutput</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span> = 
<a href="twoscomp.html#K15" title="TWOSCOMP:func.15">xor2a</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="twoscomp.html#E3:53"><i><font color="Green" title="E43">A2</font></i></a>, <a class="ref" href="facirc_1.html#T35" title="FACIRC_1:th.35">FACIRC_1:35</a></i>
<br/>.= 
<a href="twoscomp.html#K15" title="TWOSCOMP:func.15">xor2a</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font></span>)</span></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="txt" href="twoscomp.html#E4:53"><i><font color="Green" title="E44">A3</font></i></a>, <a class="txt" href="twoscomp.html#E5:53"><i><font color="Green" title="E45">A4</font></i></a>, <a class="ref" href="finseq_2.html#T145" title="FINSEQ_2:th.145">FINSEQ_2:145</a></i>
;<br/>

<b>thus </b><a NAME="E7:53"/>
( <span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> &amp; <span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font> )
 <b>by </b><i><a class="txt" href="twoscomp.html#E2:53"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="circuit2.html#D5" title="CIRCUIT2:def.5">CIRCUIT2:def 5</a></i>;<br/>


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