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

<b>let </b><font color="Maroon">a</font> be    <a href="ami_3.html#M1">Data-Location</a> ;<br/><b>let </b><font color="Maroon">i1</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>



<b>set </b><font color="Maroon">X</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Olive">il</font></span>)</span> where <font color="Olive">il</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="53_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:53_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Olive">il</font></span>)</span> where <font color="Olive">il</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span> 
 ;<br/><b>set </b><font color="Maroon">il1</font> =  <a href="ami_3.html#K16">il.</a> 1;<br/><b>set </b><font color="Maroon">il2</font> =  <a href="ami_3.html#K16">il.</a> 2;<br/><a NAME="E2:53_1_1"/>
(  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 1</span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Olive">il</font></span>)</span> where <font color="Olive">il</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span>  &amp;  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 2</span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Olive">il</font></span>)</span> where <font color="Olive">il</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span>  )
 ;<br/><a NAME="E3:53_1_1"/><b>then </b><i><font color="Green">E47</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 1</span>)</span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 2</span>)</span> )
 <b>by </b><i><a class="ref" href="ami_6.html#T6" target="_self">Th6</a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/><a NAME="E4:53_1_1"/>
(  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <span class="p3">(<span class="default"><a href="ami_3.html#K16">il.</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K2">}</a></span> &amp;  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <span class="p3">(<span class="default"><a href="ami_3.html#K16">il.</a> 2</span>)</span></span>)</span></span><a href="tarski.html#K2">}</a></span> )
 <b>by </b><i><a class="txt" href="ami_6.html#E4:53_1"><i><font color="Green">E53</font></i></a></i>;<br/><a NAME="E5:53_1_1"/><b>then </b><i><font color="Green">E49</font></i>: 
( ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 1</span>)</span> ) &amp; ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 2</span>)</span> ) )
 <b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>thus </b><a NAME="E6:53_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">i1</font></span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:53_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">i1</font></span><a href="realset1.html#K5">}</a></span>
 ;<br/><a NAME="E3:53_1"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E4:53_1"/><i><font color="Green">E53</font></i>: 
 <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Olive">il</font></span>)</span> where <font color="Olive">il</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span> 
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="53_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:53_1_2"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Olive">il</font></span>)</span> where <font color="Olive">il</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">il</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E3:53_1_2"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Maroon">il</font>
 ;<br/><a NAME="E4:53_1_2"/>
 <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Maroon">il</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="ami_6.html#E4:53_1"><i><font color="Green">E53</font></i></a></i>;<br/><b>hence </b><a NAME="E5:53_1_2"/>
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:53_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Olive">il</font></span>)</span> where <font color="Olive">il</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span> 
 <b>by </b><i><a class="ref" href="ami_6.html#T6" target="_self">Th6</a>, , <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:53"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">i1</font></span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


</div>
