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<b>let </b><font color="Maroon" title="c1">p</font> be   <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">k</font>, <font color="Olive" title="b2">loc</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <br/> for <font color="Olive" title="b3">I</font> being  <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>   st <font color="Olive" title="b2">loc</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> <span class="p1">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span> &amp; <font color="Olive" title="b3">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">loc</font> holds <br/> <a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <font color="Olive" title="b3">I</font>,<font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Olive" title="b1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b1">k</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">k</font>, <font color="Maroon" title="c3">loc</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">I</font> being  <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>   st <font color="Maroon" title="c3">loc</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> <span class="p1">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span> &amp; <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">loc</font> holds <br/> <a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <font color="Olive" title="b1">I</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">loc</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> <span class="p1">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span> &amp; <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">loc</font> implies  <a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span> )</span><br/>







<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E21">A1</font></i>: 
( <font color="Maroon" title="c3">loc</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> <span class="p1">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span> &amp; <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">loc</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span><br/>

<a NAME="E2:21"/><i><font color="Green" title="E22">A2</font></i>: 
 <a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">i</font> = <font color="Maroon" title="c3">loc</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  ;<br/>
<a NAME="E4:21"/>
<font color="Maroon" title="c5">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">j</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span> where <font color="Olive" title="b1">j</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : <font color="Olive" title="b1">j</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> <span class="p1">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span> </span>}</span> 
 
<b>by </b><i><a class="txt" href="#E1:21"><i><font color="Green" title="E21">A1</font></i></a></i>;<br/>
<a NAME="E5:21"/><b>then </b><i><font color="Green" title="E23">A4</font></i>: 
<font color="Maroon" title="c3">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</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> <span class="p1">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="reloc.html#T23" target="_self" title="RELOC:th.23">Th23</a></i>;<br/>
<a NAME="E6:21"/><i><font color="Green" title="E24">A5</font></i>: 
<font color="Maroon" title="c3">loc</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> <span class="p1">(<span class="default"><a href="reloc.html#K2" title="RELOC:func.2">IncAddr</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:21"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="reloc.html#D5" target="_self" title="RELOC:def.5">Def5</a></i>;<br/>
<a NAME="E7:21"/><i><font color="Green" title="E25">A6</font></i>: 
<font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">loc</font>
 
<b>by </b><i><a class="txt" href="#E1:21"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="#E2:21"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E8:21"/>
 <a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span>
<b>by </b><i><a class="txt" href="#E5:21"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="reloc.html#K2" title="RELOC:func.2">IncAddr</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K5" title="SCMNORM:func.5">Shift</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span>
<b>by </b><i><a class="ref" href="reloc.html#T22" target="_self" title="RELOC:th.22">Th22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmnorm.html#K5" title="SCMNORM:func.5">Shift</a> <span class="p2">(<span class="default"><a href="reloc.html#K2" title="RELOC:func.2">IncAddr</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span>
<b>by </b><i><a class="ref" href="reloc.html#T19" target="_self" title="RELOC:th.19">Th19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="reloc.html#K2" title="RELOC:func.2">IncAddr</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">loc</font>
<b>by </b><i><a class="txt" href="#E6:21"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="valued_1.html#D12" title="VALUED_1:def.12">VALUED_1:def 12</a></i>
<br/>.= 
 <a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">loc</font></span>)</span>,<font color="Maroon" title="c2">k</font>
<b>by </b><i><a class="txt" href="#E1:21"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="reloc.html#D5" target="_self" title="RELOC:def.5">Def5</a></i>
<br/>.= 
 <a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font>
<b>by </b><i><a class="txt" href="#E1:21"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="#E7:21"><i><font color="Green" title="E25">A6</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
;<br/>
<b>hence </b><a NAME="E10:21"/>
 <a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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