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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="scmring1.html#V1">good</a> <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font></span>)</span>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</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>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K2">}</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:75_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</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>then consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:75_1_1"/><i><font color="Green">E70</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</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="tarski.html#D4">TARSKI:def 4</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</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> such that </b><br/><a NAME="E5:75_1_1"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E3:75_1_1"><i><font color="Green">E70</font></i></a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:75_1_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> or ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Olive">b<sub>2</sub></font> or ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K5">AddTo</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> or ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K6">SubFrom</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> or ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K7">MultBy</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> or ex <font color="Olive">b<sub>1</sub></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">c<sub>1</sub></font></span>)</span> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Olive">b<sub>1</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></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">c<sub>1</sub></font></span>)</span> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmring2.html#K10">=0_goto</a> <font color="Olive">b<sub>2</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Olive">b<sub>2</sub></font> )
 </span><b>by </b><i><a class="ref" href="scmring2.html#T8">SCMRING2:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_1_1_1_1"><b>suppose </b></a><a NAME="E1:75_1_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span>
 ;<br/><div class="add"><a NAME="E2:75_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <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="scmring2.html#T30">SCMRING2:30</a></i>;<br/><a NAME="E3:75_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</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>2</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E3:75_1_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scmring3.html#E5:75_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmring3.html#T53" target="_self">Th53</a></i>;<br/><a NAME="E4:75_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E5:75_1_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_1_1_1_2"><b>suppose </b></a><a NAME="E1:75_1_1_1_2"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Olive">b<sub>2</sub></font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:75_1_1_1_2"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><a NAME="E4:75_1_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E3:75_1_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scmring3.html#E5:75_1_1"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scmring3.html#E3:75_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmring3.html#T54" target="_self">Th54</a></i>;<br/><a NAME="E5:75_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:75_1_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_1_1_1_3"><b>suppose </b></a><a NAME="E1:75_1_1_1_3"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K5">AddTo</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:75_1_1_1_3"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K5">AddTo</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 ;<br/><a NAME="E4:75_1_1_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5">AddTo</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E3:75_1_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scmring3.html#E5:75_1_1"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scmring3.html#E3:75_1_1_1_3"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmring3.html#T55" target="_self">Th55</a></i>;<br/><a NAME="E5:75_1_1_1_3"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:75_1_1_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_1_1_1_4"><b>suppose </b></a><a NAME="E1:75_1_1_1_4"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K6">SubFrom</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:75_1_1_1_4"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K6">SubFrom</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 ;<br/><a NAME="E4:75_1_1_1_4"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><a href="scmring2.html#K6">SubFrom</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E3:75_1_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scmring3.html#E5:75_1_1"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scmring3.html#E3:75_1_1_1_4"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmring3.html#T56" target="_self">Th56</a></i>;<br/><a NAME="E5:75_1_1_1_4"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:75_1_1_1_4"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_1_1_1_5"><b>suppose </b></a><a NAME="E1:75_1_1_1_5"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K7">MultBy</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:75_1_1_1_5"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K7">MultBy</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 ;<br/><a NAME="E4:75_1_1_1_5"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><a href="scmring2.html#K7">MultBy</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E3:75_1_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scmring3.html#E5:75_1_1"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scmring3.html#E3:75_1_1_1_5"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmring3.html#T57" target="_self">Th57</a></i>;<br/><a NAME="E5:75_1_1_1_5"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:75_1_1_1_5"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_1_1_1_6"><b>suppose </b></a><a NAME="E1:75_1_1_1_6"/>
ex <font color="Olive">b<sub>1</sub></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">c<sub>1</sub></font></span>)</span> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></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">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E3:75_1_1_1_6"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><a NAME="E4:75_1_1_1_6"/>
<font color="Maroon">c<sub>5</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>8</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E3:75_1_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scmring3.html#E5:75_1_1"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scmring3.html#E3:75_1_1_1_6"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmring3.html#T59" target="_self">Th59</a></i>;<br/><a NAME="E5:75_1_1_1_6"/><b>then </b>
<font color="Maroon">c<sub>5</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>8</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E3:75_1_1_1_6"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmring3.html#T60" target="_self">Th60</a></i>;<br/><b>hence </b><a NAME="E6:75_1_1_1_6"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T37">XBOOLE_1:37</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_1_1_1_7"><b>suppose </b></a><a NAME="E1:75_1_1_1_7"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></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">c<sub>1</sub></font></span>)</span> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmring2.html#K10">=0_goto</a> <font color="Olive">b<sub>2</sub></font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>9</sub></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">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E3:75_1_1_1_7"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmring2.html#K10">=0_goto</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><a NAME="E4:75_1_1_1_7"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>9</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E3:75_1_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scmring3.html#E5:75_1_1"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scmring3.html#E3:75_1_1_1_7"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmring3.html#T63" target="_self">Th63</a></i>;<br/><a NAME="E5:75_1_1_1_7"/><b>then </b><i><font color="Green">E73</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K1">NIC</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp; not <font color="Maroon">c<sub>5</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>9</sub></font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:75_1_1_1_7"/>
 <a href="amistd_1.html#K1">NIC</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E3:75_1_1_1_7"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmring3.html#T61" target="_self">Th61</a></i>;<br/><a NAME="E7:75_1_1_1_7"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="scmring3.html#E5:75_1_1_1_7"><i><font color="Green">E73</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E8:75_1_1_1_7"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="scmring3.html#E5:75_1_1_1_7"><i><font color="Green">E73</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_1_1_1_8"><b>suppose </b></a><a NAME="E1:75_1_1_1_8"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Olive">b<sub>2</sub></font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>9</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:75_1_1_1_8"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><a NAME="E4:75_1_1_1_8"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E3:75_1_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scmring3.html#E5:75_1_1"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scmring3.html#E3:75_1_1_1_8"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmring3.html#T58" target="_self">Th58</a></i>;<br/><a NAME="E5:75_1_1_1_8"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:75_1_1_1_8"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div><b>assume </b><a NAME="E2:75_1"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:75_1_2"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font> )
 </span><b>by </b><i><a class="txt" href="scmring3.html#E2:75_1"><i><font color="Green">E70</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_1_2_1"><b>suppose </b></a><a NAME="E1:75_1_2_1"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="ami_1.html#K5">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/><a NAME="E2:75_1_2_1"/>
<span class="p1">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <span class="p3">(<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>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T53" target="_self">Th53</a></i>;<br/><a NAME="E3:75_1_2_1"/><b>then </b>
( <font color="Maroon">c<sub>5</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>2</sub></font></span><a href="tarski.html#K1">}</a></span> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</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"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</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="txt" href="scmring3.html#E1:75_1_2_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:75_1_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</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="tarski.html#D4">TARSKI:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_1_2_2"><b>suppose </b></a><a NAME="E1:75_1_2_2"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><b>consider </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="scmring2.html#K5">AddTo</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>;<br/><a NAME="E3:75_1_2_2"/>
<span class="p1">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5">AddTo</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5">AddTo</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T55" target="_self">Th55</a></i>;<br/><a NAME="E4:75_1_2_2"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></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"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</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="txt" href="scmring3.html#E1:75_1_2_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E5:75_1_2_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</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="tarski.html#D4">TARSKI:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E2:75"/><b>then </b>
 <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</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>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>
<b>hence </b><a NAME="E3:75"/>
 <a href="amistd_1.html#K3">SUCC</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="scmring2.html#K11">Next</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 ;<br/>


</div>
