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<b>let </b><font color="Maroon">i1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">i2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">j1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">j2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>







<b>assume </b><a NAME="E1:5"/>
<font color="Maroon">i1</font>,<font color="Maroon">j1</font>,<font color="Maroon">i2</font>,<font color="Maroon">j2</font> <a href="gobrd10.html#R2" target="_self">are_adjacent2</a> 
 ;<br/>

<a NAME="E2:5"/><b>then </b>
( ( <font color="Maroon">i1</font>,<font color="Maroon">i2</font> <a href="gobrd10.html#R1" target="_self">are_adjacent1</a>  &amp; <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j2</font> ) or ( <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> &amp; <font color="Maroon">j1</font>,<font color="Maroon">j2</font> <a href="gobrd10.html#R1" target="_self">are_adjacent1</a>  ) )
 
<b>by </b><i/>;<br/>
<a NAME="E3:5"/><b>then </b>
( ( <font color="Maroon">i1</font> <a href="nat_1.html#K1">+</a> 1,<font color="Maroon">i2</font> <a href="nat_1.html#K1">+</a> 1 <a href="gobrd10.html#R1" target="_self">are_adjacent1</a>  &amp; <font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1 ) or ( <font color="Maroon">i1</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> 1,<font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1 <a href="gobrd10.html#R1" target="_self">are_adjacent1</a>  ) )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:5"/>
<font color="Maroon">i1</font> <a href="nat_1.html#K1">+</a> 1,<font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> 1,<font color="Maroon">i2</font> <a href="nat_1.html#K1">+</a> 1,<font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1 <a href="gobrd10.html#R2" target="_self">are_adjacent2</a> 
 <b>by </b><i/>;<br/>


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