<?xml version="1.0"?>
<div class="add">

<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>



<b>assume </b><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:()"><i><font color="Red">::  thesis: </font></i></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"/><b>then </b>
( <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 )
 
<b>by </b><i><a class="ref" href="gobrd10.html#D1" target="_self" title="GOBRD10:def.1">Def1</a></i>;<br/>
<b>hence </b><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> 
 <b>by </b><i><a class="ref" href="gobrd10.html#D1" target="_self" title="GOBRD10:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
