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<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>;<br/><b>let </b><font color="Maroon" title="c2">a</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>;<br/><b>let </b><font color="Maroon" title="c3">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>;<br/>





<b>set </b><font color="Maroon" title="c4">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="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">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="64_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:64_1_1"/><i><font color="Green" title="E60">A1</font></i>: 
<font color="Maroon" title="c5">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="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">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/><b>reconsider </b><font color="Maroon" title="c6">il1</font> =  <a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> 1, <font color="Maroon" title="c7">il2</font> =  <a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> 2 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="E3:64_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="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">i1</font></span>)</span>,<font color="Maroon" title="c6">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"><font color="Maroon" title="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">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>  &amp;  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">i1</font></span>)</span>,<font color="Maroon" title="c7">il2</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="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">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="E4:64_1_1"/><b>then </b><i><font color="Green" title="E61">A2</font></i>: 
( <font color="Maroon" title="c5">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="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">i1</font></span>)</span>,<font color="Maroon" title="c6">il1</font> &amp; <font color="Maroon" title="c5">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="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">i1</font></span>)</span>,<font color="Maroon" title="c7">il2</font> )
 <b>by </b><i><a class="txt" href="scmring3.html#E1:64_1_1"><i><font color="Green" title="E60">A1</font></i></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></i>;<br/><a NAME="E5:64_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="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">i1</font></span>)</span>,<font color="Maroon" title="c6">il1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">i1</font>,<span class="p2">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c6">il1</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">i1</font></span>)</span>,<font color="Maroon" title="c7">il2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">i1</font>,<span class="p2">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c7">il2</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 <b>by </b><i><a class="ref" href="scmring3.html#T61" target="_self" title="SCMRING3:th.61">Th61</a></i>;<br/><a NAME="E6:64_1_1"/><b>then </b><i><font color="Green" title="E62">A3</font></i>: 
( ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i1</font> or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c6">il1</font> ) &amp; ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i1</font> or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c7">il2</font> ) )
 <b>by </b><i><a class="txt" href="scmring3.html#E4:64_1_1"><i><font color="Green" title="E61">A2</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>thus </b><a NAME="E7:64_1_1"/>
<font color="Maroon" title="c5">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="c3">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E6:64_1_1"><i><font color="Green" title="E62">A3</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:64_1"/>
<font color="Maroon" title="c5">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="c3">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/><a NAME="E3:64_1"/><b>then </b><i><font color="Green" title="E60">A4</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">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="E4:64_1"/><i><font color="Green" title="E61">A5</font></i>: 
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">i1</font></span>)</span>,<font color="Maroon" title="c3">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"><font color="Maroon" title="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">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="64_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:64_1_2"/>
<font color="Maroon" title="c6">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="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">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="E2:64_1_2"/><b>then </b>
 ex <font color="Olive" title="b1">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> st <font color="Maroon" title="c6">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="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">i1</font></span>)</span>,<font color="Olive" title="b1">il</font>
 ;<br/><b>hence </b><a NAME="E3:64_1_2"/>
<font color="Maroon" title="c3">i1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Y</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T61" target="_self" title="SCMRING3:th.61">Th61</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:64_1"/>
<font color="Maroon" title="c5">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="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">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="scmring3.html#E3:64_1"><i><font color="Green" title="E60">A4</font></i></a>, <a class="txt" href="scmring3.html#E4:64_1"><i><font color="Green" title="E61">A5</font></i></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:64"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c3">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="c3">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>;<br/>


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