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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</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>4</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2">void</a> <a href="ami_1.html#V5">IC-Ins-separated</a> <a href="ami_1.html#V8">definite</a> <a href="amistd_1.html#V4">standard</a> <a href="amistd_2.html#V8" target="_self">regular</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be  <a href="ami_3.html#V1">programmed</a> <a href="amistd_1.html#V9">lower</a>  <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">c<sub>4</sub></font>;<br/>









<i><font color="Green">E51</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#D15" target="_self">Def15</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="amistd_2.html#D15" target="_self">Def15</a></i>
;<br/>
<a NAME="E2:89"/><i><font color="Green">E52</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="amistd_2.html#D15" target="_self">Def15</a></i>;<br/>
<a NAME="E3:89"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font> holds <br/><span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:89_2"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:89_2"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="ami_3.html#D13">AMI_3:def 13</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="txt" href="amistd_2.html#E1:89_2"><i><font color="Green">E53</font></i></a></i>;<br/>
<a NAME="E4:89_2"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="amistd_1.html#D13">AMISTD_1:def 13</a></i>;<br/>
<a NAME="E5:89_2"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E1:89_2"><i><font color="Green">E53</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self">Def15</a></i>;<br/>
<i><font color="Green">E56</font></i>:  <a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E1:89_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="amistd_2.html#E4:89_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self">Def15</a></i>
<br/>.= 
 <a href="ami_5.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E5:89_2"><i><font color="Green">E55</font></i></a>, <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>
;<br/>
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> = 
 <a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="amistd_2.html#E5:89_2"><i><font color="Green">E55</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self">Def15</a></i>
<br/>.= 
 <a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E6:89_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="amistd_2.html#T37" target="_self">Th37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E1:89_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="amistd_2.html#E4:89_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self">Def15</a></i>
;<br/>
<b>hence </b><a NAME="E8:89_2"/>
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E4:89_2"><i><font color="Green">E54</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:89"/>
 <a href="amistd_2.html#K9" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:89"><i><font color="Green">E51</font></i></a>, <a class="txt" href="amistd_2.html#E2:89"><i><font color="Green">E52</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


</div>
