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<b>let </b><font color="Maroon">c<sub>1</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>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2" target="_self">void</a> <a href="ami_1.html#V5" target="_self">IC-Ins-separated</a> <a href="ami_1.html#V7" target="_self">steady-programmed</a> <a href="ami_1.html#V8" target="_self">definite</a>  <a href="ami_1.html#L1" target="_self">AMI-Struct</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means <font color="Maroon">c<sub>3</sub></font> <a href="ami_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" target="_self">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="ami_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<a NAME="E1:76"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<b>by </b><i><a class="ref" href="ami_1.html#D19" target="_self">Def19</a></i>;<br/>
<div><i><font color="Green">E45</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:76_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>5</sub></font>]
 ;<br/><b>then </b><font color="Maroon">c<sub>3</sub></font> <a href="ami_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" target="_self">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" target="_self">CurInstr</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" target="_self">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" target="_self">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="ami_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D13" target="_self">Def13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K9" target="_self">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" target="_self">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="ami_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" target="_self">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D19" target="_self">Def19</a></i>
;<br/><b>hence </b><a NAME="E3:76_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/></div><b>end;</b></div>
<b>thus </b><a NAME="E3:76"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 <b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="ami_1.html#E1:76"><i><font color="Green">E44</font></i></a>, <a class="txt" href="ami_1.html#E2:76"><i><font color="Green">E45</font></i></a>);</i><br/>


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