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<b>let </b><font color="Maroon">R</font> be  <a href="scmring1.html#V1">good</a> <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">a</font> be    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">i1</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>;<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="scmring2.html#K10">=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 <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> : verum </span>}</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_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="E1:73_1_1"/><i><font color="Green">E50</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="scmring2.html#K10">=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 <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> : verum </span>}</span> 
 ;<br/><b>reconsider </b><font color="Maroon">il1</font> =  <a href="ami_3.html#K16">il.</a> 1, <font color="Maroon">il2</font> =  <a href="ami_3.html#K16">il.</a> 2 as   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> <b>by </b><i><a class="ref" href="ami_3.html#D1">AMI_3:def 1</a>, <a class="ref" href="scmring2.html#D1">SCMRING2:def 1</a></i>;<br/><a NAME="E3:73_1_1"/>
(  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Maroon">il1</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="scmring2.html#K10">=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 <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> : 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="scmring2.html#K10">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Maroon">il2</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="scmring2.html#K10">=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 <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> : verum </span>}</span>  )
 ;<br/><a NAME="E4:73_1_1"/><b>then </b><i><font color="Green">E51</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="scmring2.html#K10">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Maroon">il1</font> &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="scmring2.html#K10">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Maroon">il2</font> )
 <b>by </b><i>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/><a NAME="E5:73_1_1"/>
(  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Maroon">il1</font> <a href="tarski.html#R1">c=</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="scmring2.html#K11">Next</a> <font color="Maroon">il1</font></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="scmring2.html#K10">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Maroon">il2</font> <a href="tarski.html#R1">c=</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="scmring2.html#K11">Next</a> <font color="Maroon">il2</font></span>)</span></span><a href="tarski.html#K2">}</a></span> )
 <b>by </b><i><a class="txt" href="scmring3.html#E3:73_1"><i><font color="Green">E67</font></i></a></i>;<br/><a NAME="E6:73_1_1"/><b>then </b><i><font color="Green">E64</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="scmring2.html#K11">Next</a> <font color="Maroon">il1</font> ) &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="scmring2.html#K11">Next</a> <font color="Maroon">il2</font> ) )
 <b>by </b><i><a class="ref" href="scmring3.html#T8" target="_self">Th8</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E7:73_1_1"/>
<font color="Maroon">il1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">il2</font>
 <b>by </b><i><a class="ref" href="ami_3.html#T53">AMI_3:53</a></i>;<br/><b>hence </b><a NAME="E8:73_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i1</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T9" target="_self">Th9</a>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:73_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i1</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E3:73_1"/><b>then </b><i><font color="Green">E67</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="E4:73_1"/><i><font color="Green">E68</font></i>: 
 <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmring2.html#K10">=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="scmring2.html#K10">=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 <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> : verum </span>}</span> 
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_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="E1:73_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="scmring2.html#K10">=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 <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> : verum </span>}</span> 
 ;<br/><a NAME="E2:73_1_2"/><b>then </b>
 ex <font color="Olive">il</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> st <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="scmring2.html#K10">=0_goto</a> <font color="Maroon">i1</font></span>)</span>,<font color="Olive">il</font>
 ;<br/><b>hence </b><a NAME="E3:73_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="txt" href="scmring3.html#E3:73_1"><i><font color="Green">E67</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:73_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="scmring2.html#K10">=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 <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> : verum </span>}</span> 
 <b>by </b><i>, <a class="ref" href="scmring3.html#T8" target="_self">Th8</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="E2:73"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i1</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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