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

<span class="kw">let </span><font color="Maroon" title="c1">a</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">k</font> being  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  holds   <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">k</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">X</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span>  implies <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) &amp; ( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> implies <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span>  ) )</span><br/><div><span class="lab"><font color="Green" title="E47">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span>  implies <font color="Maroon" title="c2">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y</font> )</span><br/><span class="kw">assume </span><a NAME="E1:63_1_1"/>
<font color="Maroon" title="c5">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">il</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:63_1_1"/><span class="lab"><font color="Green" title="E48">A2</font></span>: 
<font color="Maroon" title="c5">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c6">il</font>
 ;<br/><a NAME="E4:63_1_1"/>
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c6">il</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c2">k</font>,<span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c6">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_6.html#T50" target="_self" title="AMI_6:th.50">Th50</a></span>;<br/><span class="kw">hence </span><a NAME="E5:63_1_1"/>
<font color="Maroon" title="c2">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63_1_1"><span class="lab"><font color="Green" title="E48">A2</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> implies <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span>  )</span>
<div class="add"><span class="kw">set </span><font color="Maroon" title="c5">il1</font> = 1;<br/><span class="kw">set </span><font color="Maroon" title="c6">il2</font> = 2;<br/><span class="kw">assume </span><a NAME="E1:63_1_2"/><span class="lab"><font color="Green" title="E48">A3</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><a NAME="E2:63_1_2"/><span class="lab"><font color="Green" title="E49">A4</font></span>: 
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c2">k</font>,<span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> 2</span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_6.html#T50" target="_self" title="AMI_6:th.50">Th50</a></span>;<br/><a NAME="E3:63_1_2"/>
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span> 
 ;<br/><a NAME="E4:63_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_1_2"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></span>;<br/><a NAME="E5:63_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A5</font></span>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> 2 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63_1_2"><span class="lab"><font color="Green" title="E49">A4</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><a NAME="E6:63_1_2"/><span class="lab"><font color="Green" title="E51">A6</font></span>: 
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c2">k</font>,<span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> 1</span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_6.html#T50" target="_self" title="AMI_6:th.50">Th50</a></span>;<br/><a NAME="E7:63_1_2"/>
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span> 
 ;<br/><a NAME="E8:63_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_1_2"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></span>;<br/><a NAME="E9:63_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:63_1_2"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E10:63_1_2"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:63_1_2"><span class="lab"><font color="Green" title="E50">A5</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E3:63_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span> </span><br/><a NAME="E4:63_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A7</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E5:63_1"/>
<font color="Maroon" title="c2">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">k</font> = <font color="Maroon" title="c2">k</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  ;<br/><a NAME="E7:63_1"/>
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c5">k</font></span>)</span>,<font color="Maroon" title="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span> 
 ;<br/><span class="kw">hence </span><a NAME="E8:63_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:63_1"><span class="lab"><font color="Green" title="E48">A7</font></span></a>, <a class="txt" href="#E1:63_1"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:63"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
