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<b>let </b><font color="Maroon" title="c1">p</font> be  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a> non <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="ami_1.html#NM7" title="AMI_1:NM.7">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/><b>let </b><font color="Maroon" title="c2">s1</font>, <font color="Maroon" title="c3">s2</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/>



<b>assume </b><a NAME="E1:42"/><i><font color="Green" title="E25">A1</font></i>: 
( <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s1</font> &amp; <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s2</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c4">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c5">da</font>, <font color="Maroon" title="c6">db</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ;<br/><b>let </b><font color="Maroon" title="c7">I</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/>





<b>assume </b><a NAME="E2:42"/><i><font color="Green" title="E26">A2</font></i>: 
<font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span>
 ;<br/>

<b>set </b><font color="Maroon" title="c8">Cs1i</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font>;<br/>
<b>set </b><font color="Maroon" title="c9">Cs2i</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font>;<br/>
<a NAME="E3:42"/><i><font color="Green" title="E27">A3</font></i>: 
<font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E1:42"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="ami_5.html#E2:42"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="ami_5.html#T87" target="_self" title="AMI_5:th.87">Th87</a></i>;<br/>
<b>set </b><font color="Maroon" title="c10">Cs1i1</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c11">Cs2i1</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<i><font color="Green" title="E28">A4</font></i>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span>

;<br/>
<i><font color="Green" title="E29">A5</font></i>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span>

;<br/>
<a NAME="E6:42"/><i><font color="Green" title="E30">A6</font></i>: 
( <font color="Maroon" title="c5">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font> implies ( <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="c2">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> &amp; <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="c3">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> ) )
 
<b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/>
<b>assume </b><a NAME="E7:42"/><i><font color="Green" title="E31">A7</font></i>: 
( <font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <font color="Maroon" title="c5">da</font>,<font color="Maroon" title="c6">db</font> &amp; <font color="Maroon" title="c5">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font> &amp; <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="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span> )
 ;<br/>

<a NAME="E8:42"/><b>then </b>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="ami_5.html#E2:42"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="ami_5.html#E3:42"><i><font color="Green" title="E27">A3</font></i></a>, <a class="txt" href="ami_5.html#E4:42"><i><font color="Green" title="E28">A4</font></i></a>, <a class="txt" href="ami_5.html#E5:42"><i><font color="Green" title="E29">A5</font></i></a>, <a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></i>;<br/>
<b>hence </b><a NAME="E9:42"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_5.html#E1:42"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="ami_5.html#E6:42"><i><font color="Green" title="E30">A6</font></i></a>, <a class="txt" href="ami_5.html#E7:42"><i><font color="Green" title="E31">A7</font></i></a>, <a class="ref" href="ami_1.html#D25" title="AMI_1:def.25">AMI_1:def 25</a></i>;<br/>


</div>
