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

<a NAME="E1:16"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">i</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : verum </span>}</span>  <a href="xboole_0.html#K3">/\</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : <font color="Olive">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">i</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : verum </span>}</span>  <a href="xboole_0.html#K3">/\</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : <font color="Olive">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span> ;<br/>
<b>assume </b><a NAME="E2:16_1"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">i</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : verum </span>}</span>  <a href="xboole_0.html#K3">/\</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : <font color="Olive">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E3:16_1"/><b>then </b><i><font color="Green">E34</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">i</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : verum </span>}</span>  &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : <font color="Olive">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">i</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:16_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">i</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/>
<b>consider </b><font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E7:16_1"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">l</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E9:16_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">l</font> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i>, <a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/>
<b>reconsider </b><font color="Maroon">l</font> = <font color="Maroon">l</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E11:16_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">l</font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i>, </i>;<br/>
<a NAME="E12:16_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K15">dl.</a> <font color="Maroon">i</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <font color="Maroon">l</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E13:16_1"/>
contradiction
 <b>by </b><i><a class="ref" href="scm_1.html#T7">SCM_1:7</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:16"/>
 <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#R1">misses</a>  <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_2.html#D2">AMI_2:def 2</a>, <a class="ref" href="ami_2.html#D3">AMI_2:def 3</a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>


</div>
