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<span class="kw">let </span><font color="Maroon" title="c3">I</font> be   <a href="scmnorm.html#NM1" title="SCMNORM:NM.1">preProgram</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b2">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c3">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Olive" title="b2">a</font> holds <br/> <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K2" title="SCMFSA_5:func.2">Relocated</a> <font color="Maroon" title="c3">I</font>,<font color="Olive" title="b1">n</font></span>)</span> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Olive" title="b2">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <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"> for <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c3">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Olive" title="b1">a</font> holds <br/> <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K2" title="SCMFSA_5:func.2">Relocated</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Olive" title="b1">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">a</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</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> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Maroon" title="c5">a</font> implies  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K2" title="SCMFSA_5:func.2">Relocated</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Maroon" title="c5">a</font> )</span><br/>





<span class="lab"><font color="Green" title="E13">A1</font></span>:  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K2" title="SCMFSA_5:func.2">Relocated</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span> = 
 <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Reloc</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">I</font></span>)</span>,<font color="Maroon" title="c4">n</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_5.html#T2" title="SCMFSA_5:th.2">SCMFSA_5:2</a></span>
<br/>.= 
 <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Reloc</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T105" title="AMI_1:th.105">AMI_1:105</a></span>
<br/>.= 
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span>,<font color="Maroon" title="c4">n</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_4.html#T35" title="SCMFSA_4:th.35">SCMFSA_4:35</a></span>
;<br/>
<a NAME="E2:22"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_4.html#D6" title="SCMFSA_4:def.6">SCMFSA_4:def 6</a></span>;<br/>
<a NAME="E3:22"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c4">n</font></span>)</span> where <font color="Olive" title="b1">m</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  : <font color="Olive" title="b1">m</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="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span> </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D12" title="VALUED_1:def.12">VALUED_1:def 12</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:22"/><span class="lab"><font color="Green" title="E16">A4</font></span>: 
<font color="Maroon" title="c3">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Maroon" title="c5">a</font>
 ; <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#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K2" title="SCMFSA_5:func.2">Relocated</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Maroon" title="c5">a</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">i</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K2" title="SCMFSA_5:func.2">Relocated</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span></span>)</span> implies <font color="Maroon" title="c6">i</font> <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">does_not_destroy</a> <font color="Maroon" title="c5">a</font> )</span><br/><span class="kw">assume </span><a NAME="E1:22_2"/>
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K2" title="SCMFSA_5:func.2">Relocated</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span></span>)</span>
 ; <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="c6">i</font> <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">does_not_destroy</a> <font color="Maroon" title="c5">a</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:22_2"/><span class="lab"><font color="Green" title="E17">A5</font></span>: 
<font color="Maroon" title="c7">x</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="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span>,<font color="Maroon" title="c4">n</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:22_2"/><span class="lab"><font color="Green" title="E18">A6</font></span>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c8">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E6:22_2"/><span class="lab"><font color="Green" title="E19">A7</font></span>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c4">n</font>
 <span class="kw">and </span><br/><a NAME="E7:22_2"/><span class="lab"><font color="Green" title="E20">A8</font></span>: 
<font color="Maroon" title="c8">m</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="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E3:22_2"><span class="lab"><font color="Green" title="E17">A5</font></span></a></span>;<br/><a NAME="E8:22_2"/><span class="lab"><font color="Green" title="E21">A9</font></span>: 
<font color="Maroon" title="c3">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E7:22_2"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/><a NAME="E9:22_2"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">ii</font> = <font color="Maroon" title="c3">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">m</font> as   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:22_2"><span class="lab"><font color="Green" title="E21">A9</font></span></a></span>;<br/><a NAME="E11:22_2"/><span class="lab"><font color="Green" title="E22">A10</font></span>: 
<font color="Maroon" title="c9">ii</font> <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">does_not_destroy</a> <font color="Maroon" title="c5">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E8:22_2"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="ref" href="scmfsa7b.html#D4" title="SCMFSA7B:def.4">SCMFSA7B:def 4</a></span>;<br/><font color="Maroon" title="c6">i</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_2"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E6:22_2"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E7:22_2"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="ref" href="valued_1.html#D12" title="VALUED_1:def.12">VALUED_1:def 12</a></span>
<br/>.= 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c8">m</font></span>)</span>,<font color="Maroon" title="c4">n</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E7:22_2"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="ref" href="scmfsa_4.html#D6" title="SCMFSA_4:def.6">SCMFSA_4:def 6</a></span>
<br/>.= 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c9">ii</font>,<font color="Maroon" title="c4">n</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E7:22_2"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
;<br/><span class="kw">hence </span><a NAME="E13:22_2"/>
<font color="Maroon" title="c6">i</font> <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">does_not_destroy</a> <font color="Maroon" title="c5">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:22_2"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="ref" href="scmfsa8a.html#T22" target="_self" title="SCMFSA8A:th.22">Th22</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:22"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K2" title="SCMFSA_5:func.2">Relocated</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Maroon" title="c5">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#D4" title="SCMFSA7B:def.4">SCMFSA7B:def 4</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/>


</div>
