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

<b>let </b><font color="Maroon" title="c1">R</font> be  <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a> <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">i1</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> holds   <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Olive" title="b1">i1</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">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><b>let </b><font color="Maroon" title="c2">i1</font> be    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</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">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/>



<b>set </b><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"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> : verum </span>}</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1"><b>now </b></a><div class="add"><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> : 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">i1</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">i1</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"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> : verum </span>}</span>  ) )</span><br/><div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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">i1</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"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> : verum </span>}</span>  )</span>
<div class="add"><b>assume </b><a NAME="E1:59_1_1"/><i><font color="Green" title="E57">A1</font></i>: 
<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"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> : verum </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><b>reconsider </b><font color="Maroon" title="c5">il1</font> =  <a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> 1 as    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/><a NAME="E3:59_1_1"/>
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Maroon" title="c5">il1</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"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> : verum </span>}</span> 
 ;<br/><a NAME="E4:59_1_1"/><b>then </b>
<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"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Maroon" title="c5">il1</font>
 <b>by </b><i><a class="txt" href="#E1:59_1_1"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></i>;<br/><b>hence </b><a NAME="E5:59_1_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">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T59" target="_self" title="SCMRING3:th.59">Th59</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>
<b>end;</b></div><b>assume </b><a NAME="E2:59_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">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> : verum </span>}</span> </span><br/><a NAME="E3:59_1"/><b>then </b><i><font color="Green" title="E57">A2</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">i1</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E4:59_1"/><i><font color="Green" title="E58">A3</font></i>: 
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Maroon" title="c2">i1</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"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> : verum </span>}</span> 
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_2"><b>now </b></a><div class="add"><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> : verum </span>}</span>  implies <font color="Maroon" title="c2">i1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y</font> )</span><br/><b>assume </b><a NAME="E1:59_1_2"/>
<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"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> : verum </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">i1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y</font></span><br/><b>then consider </b><font color="Maroon" title="c6">il</font> being    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E3:59_1_2"/><i><font color="Green" title="E59">A4</font></i>: 
<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"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Maroon" title="c6">il</font>
 ;<br/><a NAME="E4:59_1_2"/>
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</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#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T59" target="_self" title="SCMRING3:th.59">Th59</a></i>;<br/><b>hence </b><a NAME="E5:59_1_2"/>
<font color="Maroon" title="c2">i1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y</font>
 <b>by </b><i><a class="txt" href="#E3:59_1_2"><i><font color="Green" title="E59">A4</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</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><b>end;</b></div><b>hence </b><a NAME="E6:59_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"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</font></span>)</span>,<font color="Olive" title="b1">il</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> : verum </span>}</span> 
 <b>by </b><i><a class="txt" href="#E3:59_1"><i><font color="Green" title="E57">A2</font></i></a>, <a class="txt" href="#E4:59_1"><i><font color="Green" title="E58">A3</font></i></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</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><b>end;</b></div>
<b>hence </b><a NAME="E2:59"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c2">i1</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">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</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>
