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<b>consider </b><font color="Maroon">i</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E2:25_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/>
<b>reconsider </b><font color="Maroon">n'</font> = <font color="Maroon">n</font>, <font color="Maroon">k'</font> = <font color="Maroon">k</font>, <font color="Maroon">i</font> = <font color="Maroon">i</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>set </b><font color="Maroon">o</font> =  <a href="facirc_1.html#K16">BitAdderOutput</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span>;<br/>
<a NAME="E4:25_1_1"/><i><font color="Green">E37</font></i>: 
 <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><font color="Maroon">k'</font> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><font color="Maroon">n'</font> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:25_1_1"/><i><font color="Green">E38</font></i>: 
 <a href="facirc_1.html#K16">BitAdderOutput</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K23">BitAdderWithOverflowStr</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="facirc_1.html#T90">FACIRC_1:90</a></i>;<br/>
<a NAME="E6:25_1_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">k</font> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="circcomb.html#K3">+*</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K23">BitAdderWithOverflowStr</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">o</font> =  <a href="facirc_1.html#K16">BitAdderOutput</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="facirc_1.html#K23">BitAdderWithOverflowStr</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span></span>)</span> <b>by </b><i/>;<br/>
<a NAME="E8:25_1_1"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="facirc_1.html#K23">BitAdderWithOverflowStr</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="circcomb.html#D2">CIRCCOMB:def 2</a></i>;<br/>
<a NAME="E9:25_1_1"/><b>then </b>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E10:25_1_1"/><b>then </b>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="circcomb.html#T19">CIRCCOMB:19</a></i>;<br/>
<b>hence </b><a NAME="E11:25_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="facirc_2.html#K4" target="_self">-BitAdderStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> ex <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="facirc_1.html#K16">BitAdderOutput</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive">i</font> <a href="facirc_2.html#K6" target="_self">-BitMajorityOutput</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> )
 <b>by </b><i>, </i>;<br/>


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