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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#V4" target="_self">halting</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>given </b><font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><a NAME="E1:79"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="ami_1.html#K13" target="_self">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" target="_self">IC</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>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5" target="_self">halt</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<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>4</sub></font>;<br/>
<i><font color="Green">E46</font></i>:  <a href="ami_1.html#K8" target="_self">CurInstr</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">c<sub>4</sub></font></span>)</span> = 
<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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K13" target="_self">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" target="_self">IC</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>4</sub></font></span>)</span></span>)</span>

<br/>.= 
 <a href="ami_1.html#K5" target="_self">halt</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="ami_1.html#E1:79"><i><font color="Green">E45</font></i></a>, <a class="ref" href="ami_1.html#T54" target="_self">Th54</a></i>
;<br/>
<b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="79_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:79_2_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="79_2_1_1"><b>suppose </b></a><a NAME="E1:79_2_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:79_2_1_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/><a NAME="E4:79_2_1_1"/><i><font color="Green">E48</font></i>: 
<span class="p1">(<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>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" target="_self">Computation</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>6</sub></font></span>)</span></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="ami_1.html#E3:79_2_1_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="ami_1.html#T51" target="_self">Th51</a></i>;<br/><a NAME="E5:79_2_1_1"/><b>then </b><i><font color="Green">E49</font></i>: 
<span class="p1">(<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>6</sub></font> is <a href="ami_1.html#V9" target="_self">halting</a>
 <b>by </b><i><a class="txt" href="ami_1.html#E2:79"><i><font color="Green">E46</font></i></a>, <a class="ref" href="ami_1.html#D20" target="_self">Def20</a></i>;<br/><b>thus </b> <a href="ami_1.html#K12" target="_self">Result</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<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>4</sub></font>
<b>by </b><i><a class="txt" href="ami_1.html#E1:79"><i><font color="Green">E45</font></i></a>, <a class="ref" href="ami_1.html#T56" target="_self">Th56</a></i>
<br/>.= 
 <a href="ami_1.html#K12" target="_self">Result</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">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ami_1.html#E2:79"><i><font color="Green">E46</font></i></a>, <a class="txt" href="ami_1.html#E4:79_2_1_1"><i><font color="Green">E48</font></i></a>, <a class="txt" href="ami_1.html#E5:79_2_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="ami_1.html#D22" target="_self">Def22</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="79_2_1_2"><b>suppose </b></a><a NAME="E1:79_2_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><a NAME="E2:79_2_1_2"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1">(<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>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<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>4</sub></font>
 <b>by </b><i><a class="txt" href="ami_1.html#E2:79"><i><font color="Green">E46</font></i></a>, <a class="ref" href="ami_1.html#T52" target="_self">Th52</a></i>;<br/><a NAME="E3:79_2_1_2"/><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" target="_self">Computation</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>4</sub></font></span>)</span></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> 0 <a href="hidden.html#R1">=</a> <span class="p1">(<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>4</sub></font>
 <b>by </b><i><a class="ref" href="ami_1.html#D19" target="_self">Def19</a></i>;<br/><a NAME="E4:79_2_1_2"/><b>then </b><i><font color="Green">E49</font></i>: 
<span class="p1">(<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>6</sub></font> is <a href="ami_1.html#V9" target="_self">halting</a>
 <b>by </b><i><a class="txt" href="ami_1.html#E2:79"><i><font color="Green">E46</font></i></a>, <a class="txt" href="ami_1.html#E2:79_2_1_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="ami_1.html#D20" target="_self">Def20</a></i>;<br/><b>thus </b> <a href="ami_1.html#K12" target="_self">Result</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<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>4</sub></font>
<b>by </b><i><a class="txt" href="ami_1.html#E1:79"><i><font color="Green">E45</font></i></a>, <a class="ref" href="ami_1.html#T56" target="_self">Th56</a></i>
<br/>.= 
 <a href="ami_1.html#K12" target="_self">Result</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">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ami_1.html#E2:79"><i><font color="Green">E46</font></i></a>, <a class="txt" href="ami_1.html#E2:79_2_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="ami_1.html#E3:79_2_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="ami_1.html#E4:79_2_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="ami_1.html#D22" target="_self">Def22</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:79"/>
 <a href="ami_1.html#K12" target="_self">Result</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K12" target="_self">Result</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">c<sub>6</sub></font></span>)</span>
 ;<br/>


</div>
