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<b>let </b><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c3">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>





<b>assume </b><a NAME="E1:65"/><i><font color="Green" title="E49">A1</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> non <a href="ami_1.html#V2" title="AMI_1:attr.2">void</a> <a href="ami_1.html#V4" title="AMI_1:attr.4">halting</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">steady-programmed</a> <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c3">N</font>;<br/><b>let </b><font color="Maroon" title="c5">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c4">S</font>;<br/>



<b>assume </b><a NAME="E2:65"/><i><font color="Green" title="E50">A2</font></i>: 
<font color="Maroon" title="c5">s</font> <a href="ami_3.html#R2" title="AMI_3:pred.2">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c1">i</font></span>)</span>
 ;<br/>

<a NAME="E3:65"/><b>then </b>
<font color="Maroon" title="c5">s</font> <a href="ami_3.html#R2" title="AMI_3:pred.2">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c2">j</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_3.html#E1:65"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="ami_3.html#T45" target="_self" title="AMI_3:th.45">Th45</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c2">j</font> = 
 <a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c5">s</font>
<b>by </b><i><a class="ref" href="ami_3.html#T44" target="_self" title="AMI_3:th.44">Th44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c1">i</font>
<b>by </b><i><a class="txt" href="ami_3.html#E2:65"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="ami_3.html#T44" target="_self" title="AMI_3:th.44">Th44</a></i>
;<br/><br/>


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