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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="binarith.html#NM1">Tuple</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="margrel1.html#K6">BOOLEAN</a> ;<br/>



<a NAME="E1:25"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binari_2.html#K7" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="binarith.html#K4">'xor'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binari_2.html#K3" target="_self">Neg2</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K4">'xor'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K7">carry</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="binari_2.html#K3" target="_self">Neg2</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="binari_2.html#D6" target="_self">Def6</a></i>;<br/>
<b>hence </b><a NAME="E2:25"/>
<font color="Maroon">c<sub>2</sub></font> <a href="binari_2.html#K7" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="binarith.html#K10">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" target="_self">Neg2</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="binarith.html#D8">BINARITH:def 8</a></i>;<br/>


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