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<b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>



<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E2:65"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5" target="_self">il.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="amistd_1.html#T26" target="_self">Th26</a></i>;<br/>
<a NAME="E3:65"/><i><font color="Green">E34</font></i>: 
<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="txt" href="amistd_1.html#E2:65"><i><font color="Green">E33</font></i></a>, <a class="ref" href="amistd_1.html#T37" target="_self">Th37</a></i>;<br/>
<a NAME="E4:65"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K7" target="_self">locnum</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="amistd_1.html#E2:65"><i><font color="Green">E33</font></i></a>, <a class="ref" href="amistd_1.html#D13" target="_self">Def13</a></i>;<br/>
<b>thus </b> <a href="amistd_1.html#K3" target="_self">SUCC</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="tarski.html#K2">}</a></span>
<b>by </b><i><a class="txt" href="amistd_1.html#E3:65"><i><font color="Green">E34</font></i></a>, <a class="ref" href="amistd_1.html#T24" target="_self">Th24</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" target="_self">il.</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="amistd_1.html#T37" target="_self">Th37</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" target="_self">il.</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" target="_self">il.</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span><a href="domain_1.html#K7">}</a></span>
<b>by </b><i><a class="ref" href="amistd_1.html#T37" target="_self">Th37</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K9" target="_self">NextLoc</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K7">}</a></span>
<b>by </b><i><a class="txt" href="amistd_1.html#E2:65"><i><font color="Green">E33</font></i></a>, <a class="txt" href="amistd_1.html#E4:65"><i><font color="Green">E35</font></i></a></i>
;<br/>


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