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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#NM3">Instruction</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>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM4">State</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>assume </b><a NAME="E1:63"/><i><font color="Green">E33</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="amistd_1.html#K7" target="_self">locnum</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<a NAME="E2:63"/><i><font color="Green">E34</font></i>: 
(  <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>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7" target="_self">locnum</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K7" target="_self">locnum</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> &amp;  <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>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7" target="_self">locnum</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K7" target="_self">locnum</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i><a class="ref" href="amistd_1.html#T37" target="_self">Th37</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> =  <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="ref" href="amistd_1.html#D11" target="_self">Def11</a></i>;<br/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
 <a href="ordinal1.html#K1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_1.html#E1:63"><i><font color="Green">E33</font></i></a>, <a class="txt" href="amistd_1.html#E34"><i><font color="Green">Lemma16</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="card_1.html#T52">CARD_1:52</a></i>
;<br/>
<b>hence </b><a NAME="E5:63"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K9" target="_self">NextLoc</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_1.html#E2:63"><i><font color="Green">E34</font></i></a>, <a class="ref" href="amistd_1.html#D13" target="_self">Def13</a></i>;<br/>


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