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

<b>let </b><font color="Maroon" title="c1">k</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span><br/>

<a NAME="E1:4"/>
<font color="Maroon" title="c1">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="nat_2.html#T21" title="NAT_2:th.21">NAT_2:21</a></i>;<br/>
<b>hence </b><a NAME="E2:4"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1
 <b>by </b><i><a class="ref" href="nat_d.html#T38" title="NAT_D:th.38">NAT_D:38</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>
