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<b>set </b><font color="Maroon">c<sub>2</sub></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"><a href="ami_1.html#K5">halt</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> where B 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">c<sub>1</sub></font></span>)</span> : verum </span>}</span> ;<br/>
<b>assume </b><a NAME="E1:57_1_1"/>
not  <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5">halt</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<a NAME="E2:57_1_1"/><b>then </b>
not  <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"><a href="ami_1.html#K5">halt</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> where B 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">c<sub>1</sub></font></span>)</span> : verum </span>}</span>  is <a href="xboole_0.html#V1">empty</a>
 
;<br/>
<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:57_1_1"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>3</sub></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"><a href="ami_1.html#K5">halt</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> where B 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">c<sub>1</sub></font></span>)</span> : verum </span>}</span> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="ami_3.html#K16">il.</a> 1, <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></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="E6:57_1_1"/>
(  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5">halt</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>4</sub></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"><a href="ami_1.html#K5">halt</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> where B 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">c<sub>1</sub></font></span>)</span> : verum </span>}</span>  &amp;  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5">halt</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>5</sub></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"><a href="ami_1.html#K5">halt</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> where B 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">c<sub>1</sub></font></span>)</span> : verum </span>}</span>  )
 
;<br/>
<a NAME="E7:57_1_1"/><b>then </b>
( <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K1">}</a></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"><a href="ami_1.html#K5">halt</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> where B 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">c<sub>1</sub></font></span>)</span> : verum </span>}</span>  &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></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"><a href="ami_1.html#K5">halt</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> where B 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">c<sub>1</sub></font></span>)</span> : verum </span>}</span>  )
 
<b>by </b><i><a class="ref" href="scmring3.html#T53" target="_self">Th53</a></i>;<br/>
<a NAME="E8:57_1_1"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="txt" href="scmring3.html#E4:57_1_1"><i><font color="Green">E60</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<a NAME="E9:57_1_1"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E10:57_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="ami_3.html#T53">AMI_3:53</a></i>;<br/>


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