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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="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/>



<i><font color="Green">E7</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> = 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K7">IncAddr</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K8">Shift</a> <span class="p3">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_5.html#T2">SCMFSA_5:2</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K7">IncAddr</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K8">Shift</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#T72">AMI_5:72</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K8">Shift</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#D6">SCMFSA_4:def 6</a></i>
<br/>.= 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> :  <a href="scmfsa_2.html#K5">insloc</a> <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>2</sub></font> </span>}</span> 
<b>by </b><i><a class="ref" href="scmfsa_4.html#D7">SCMFSA_4:def 7</a></i>
;<br/>
<b>assume </b><a NAME="E2:17"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:17"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E5:17"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> :  <a href="scmfsa_2.html#K5">insloc</a> <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>2</sub></font> </span>}</span> 
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E1:17"><i><font color="Green">E7</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E7:17"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E8:17"/>
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E5:17"><i><font color="Green">E9</font></i></a></i>;<br/>
<a NAME="E9:17"/>
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:17"><i><font color="Green">E8</font></i></a>, <a class="txt" href="scmfsa6a.html#E7:17"><i><font color="Green">E10</font></i></a>, <a class="ref" href="scmfsa6a.html#T15" target="_self">Th15</a></i>;<br/>
<b>hence </b><a NAME="E10:17"/>
contradiction
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>


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