<?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#NM1" title="AMI_3:NM.1">Data-Location</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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#K9" title="AMI_3:func.9">&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#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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#K9" title="AMI_3:func.9">&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#K9" title="AMI_3:func.9">&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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span> ;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="29_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( ( <font color="Olive" title="b1">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#K9" title="AMI_3:func.9">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b2">il</font>)</span>)</span> where <font color="Olive" title="b2">il</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span>  implies <font color="Olive" title="b1">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="Olive" title="b1">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="Olive" title="b1">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#K9" title="AMI_3:func.9">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b2">il</font>)</span>)</span> where <font color="Olive" title="b2">il</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span>  ) )</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">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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#K9" title="AMI_3:func.9">&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="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K9" title="AMI_3:func.9">&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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span>  ) )</span><br/><div><span class="lab"><font color="Green" title="E12">A1</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="29_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">Y</font> <a href="tarski.html#R2" title="TARSKI: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#K9" title="AMI_3:func.9">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Olive" title="b2">il</font>)</span>)</span> where <font color="Olive" title="b2">il</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span>  holds <br/><font color="Maroon" title="c2">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">Y</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">Y</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">Y</font> <a href="tarski.html#R2" title="TARSKI: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#K9" title="AMI_3:func.9">&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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span>  implies <font color="Maroon" title="c2">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">Y</font> )</span><br/><span class="kw">assume </span><a NAME="E1:29_1_1"/>
<font color="Maroon" title="c5">Y</font> <a href="tarski.html#R2" title="TARSKI: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#K9" title="AMI_3:func.9">&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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">k</font> <a href="tarski.html#R2" title="TARSKI: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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:29_1_1"/><span class="lab"><font color="Green" title="E13">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#K9" title="AMI_3:func.9">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c6">il</font>)
 ;<br/><a NAME="E4:29_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#K9" title="AMI_3:func.9">&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"><font color="Maroon" title="c6">il</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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#T19" target="_self" onmouseover="rs('ami_6/T19')" onmouseout="rh()">Th19</a></span>;<br/><span class="kw">hence </span><a NAME="E5:29_1_1"/>
<font color="Maroon" title="c2">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:29_1_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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#K9" title="AMI_3:func.9">&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="ordinal1.html#NM6" title="ORDINAL1:NM.6">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="E1:29_1_2"/><span class="lab"><font color="Green" title="E13">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#K9" title="AMI_3:func.9">&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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="E2:29_1_2"/><span class="lab"><font color="Green" title="E14">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#K9" title="AMI_3:func.9">&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">2 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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#T19" target="_self" onmouseover="rs('ami_6/T19')" onmouseout="rh()">Th19</a></span>;<br/><a NAME="E3:29_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#K9" title="AMI_3:func.9">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,2) <a href="tarski.html#R2" title="TARSKI: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#K9" title="AMI_3:func.9">&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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span> 
 ;<br/><a NAME="E4:29_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#K9" title="AMI_3:func.9">&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="#E1:29_1_2"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="setfam_1.html#D1" onmouseover="rs('setfam_1/D1')" onmouseout="rh()">SETFAM_1:def 1</a></span>;<br/><a NAME="E5:29_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">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> 2 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29_1_2"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><a NAME="E6:29_1_2"/><span class="lab"><font color="Green" title="E16">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#K9" title="AMI_3:func.9">&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">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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#T19" target="_self" onmouseover="rs('ami_6/T19')" onmouseout="rh()">Th19</a></span>;<br/><a NAME="E7:29_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#K9" title="AMI_3:func.9">&gt;0_goto</a> <font color="Maroon" title="c2">k</font></span>)</span>,1) <a href="tarski.html#R2" title="TARSKI: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#K9" title="AMI_3:func.9">&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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span> 
 ;<br/><a NAME="E8:29_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#K9" title="AMI_3:func.9">&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="#E1:29_1_2"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="setfam_1.html#D1" onmouseover="rs('setfam_1/D1')" onmouseout="rh()">SETFAM_1:def 1</a></span>;<br/><a NAME="E9:29_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> 1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:29_1_2"><span class="lab"><font color="Green" title="E16">A6</font></span></a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E10:29_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="#E5:29_1_2"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E3:29_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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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#K9" title="AMI_3:func.9">&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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span> </span><br/><a NAME="E4:29_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">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" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><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="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" onmouseover="rs('ordinal1/D12')" onmouseout="rh()">ORDINAL1:def 12</a></span>;<br/><a NAME="E6:29_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#K9" title="AMI_3:func.9">&gt;0_goto</a> <font color="Maroon" title="c5">k</font></span>)</span>,<font color="Maroon" title="c5">k</font>) <a href="tarski.html#R2" title="TARSKI: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#K9" title="AMI_3:func.9">&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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span> 
 ;<br/><span class="kw">hence </span><a NAME="E7:29_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#K9" title="AMI_3:func.9">&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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:29_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E1:29_1"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="setfam_1.html#D1" onmouseover="rs('setfam_1/D1')" onmouseout="rh()">SETFAM_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:29"/>
 <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#K9" title="AMI_3:func.9">&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" onmouseover="rs('tarski/T2')" onmouseout="rh()">TARSKI:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
