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<span class="kw">let </span><font color="Maroon" title="c1">i1</font>, <font color="Maroon" title="c2">i2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">i2</font> <a href="gobrd10.html#R1" title="GOBRD10:pred.1">are_adjacent1</a>  implies <font color="Maroon" title="c1">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1,<font color="Maroon" title="c2">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="gobrd10.html#R1" title="GOBRD10:pred.1">are_adjacent1</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:2"/>
<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">i2</font> <a href="gobrd10.html#R1" title="GOBRD10:pred.1">are_adjacent1</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1,<font color="Maroon" title="c2">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="gobrd10.html#R1" title="GOBRD10:pred.1">are_adjacent1</a> </span><br/>

<a NAME="E2:2"/><span class="kw">then </span>
( <font color="Maroon" title="c2">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gobrd10.html#D1" target="_self" title="GOBRD10:def.1">Def1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:2"/>
<font color="Maroon" title="c1">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1,<font color="Maroon" title="c2">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="gobrd10.html#R1" title="GOBRD10:pred.1">are_adjacent1</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gobrd10.html#D1" target="_self" title="GOBRD10:def.1">Def1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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