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<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>set </b><font color="Maroon">S1</font> =  <a href="facirc_1.html#K12" target="_self">2GatesCircStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<a href="facirc_1.html#K1" target="_self">'xor'</a> ;<br/>
<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/>

<b>assume </b><a NAME="E1:132"/>
<font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="facirc_1.html#K23" target="_self">BitAdderWithOverflowStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:132"/><b>then </b>
( <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="facirc_1.html#K12" target="_self">2GatesCircStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<a href="facirc_1.html#K1" target="_self">'xor'</a> </span>)</span> &amp; <font color="Maroon">y</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="facirc_1.html#K12" target="_self">2GatesCircStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<a href="facirc_1.html#K1" target="_self">'xor'</a> </span>)</span> &amp; <font color="Maroon">c</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="facirc_1.html#K12" target="_self">2GatesCircStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<a href="facirc_1.html#K1" target="_self">'xor'</a> </span>)</span> &amp; <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K12" target="_self">2GatesCircStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<a href="facirc_1.html#K1" target="_self">'xor'</a> </span>)</span> <a href="circcomb.html#K3">+*</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K19" target="_self">MajorityStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:132"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> )
 <b>by </b><i/>;<br/>


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