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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>







<b>assume </b><a NAME="E1:6"/><i><font color="Green">E6</font></i>: 
( <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="gobrd10.html#R2" target="_self">are_adjacent2</a>  &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<a NAME="E2:6"/><b>then </b>
( ( <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="gobrd10.html#R1" target="_self">are_adjacent1</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="gobrd10.html#R1" target="_self">are_adjacent1</a>  ) )
 
<b>by </b><i><a class="ref" href="gobrd10.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E3:6"/><b>then </b>
( ( <font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1,<font color="Maroon">c<sub>2</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="gobrd10.html#R1" target="_self">are_adjacent1</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1 ) or ( <font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="binarith.html#K5">-'</a> 1 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1,<font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="gobrd10.html#R1" target="_self">are_adjacent1</a>  ) )
 
<b>by </b><i><a class="txt" href="gobrd10.html#E1:6"><i><font color="Green">E6</font></i></a>, <a class="ref" href="gobrd10.html#T2" target="_self">Th2</a></i>;<br/>
<b>hence </b><a NAME="E4:6"/>
<font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1,<font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1,<font color="Maroon">c<sub>2</sub></font> <a href="binarith.html#K5">-'</a> 1,<font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="gobrd10.html#R2" target="_self">are_adjacent2</a> 
 <b>by </b><i><a class="ref" href="gobrd10.html#D2" target="_self">Def2</a></i>;<br/>


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