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<span class="kw">let </span><font color="Maroon" title="c1">N</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">S</font> being  <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font><br/> for <font color="Olive" title="b2">I</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b2">I</font> is  <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>  holds <br/><font color="Olive" title="b2">I</font> is  <a href="amistd_2.html#V10" title="AMISTD_2:attr.10">Exec-preserving</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">I</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <font color="Maroon" title="c2">S</font>  st <font color="Olive" title="b1">I</font> is  <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>  holds <br/><font color="Olive" title="b1">I</font> is  <a href="amistd_2.html#V10" title="AMISTD_2:attr.10">Exec-preserving</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">I</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">I</font> is  <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>  implies <font color="Maroon" title="c3">I</font> is  <a href="amistd_2.html#V10" title="AMISTD_2:attr.10">Exec-preserving</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:103"/><span class="lab"><font color="Green" title="E49">A1</font></span>: 
for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c2">S</font> holds   <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">I</font> is  <a href="amistd_2.html#V10" title="AMISTD_2:attr.10">Exec-preserving</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">s1</font>, <font color="Maroon" title="c5">s2</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c2">S</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="amistd_2.html#D19" target="_self" title="AMISTD_2:def.19">AMISTD_2:def 19</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">s1</font>,<font color="Maroon" title="c5">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  implies  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">s1</font>, <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c5">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:103"/><span class="lab"><font color="Green" title="E50">A2</font></span>: 
<font color="Maroon" title="c4">s1</font>,<font color="Maroon" title="c5">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">s1</font>, <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c5">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><br/>

<a NAME="E3:103"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:103"><span class="lab"><font color="Green" title="E49">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:103"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">s1</font>, <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c5">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:103"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="txt" href="#E2:103"><span class="lab"><font color="Green" title="E50">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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