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<span class="kw">let </span><font color="Maroon" title="c5">I</font> be   <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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  not <font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Olive" title="b2">a</font> holds <br/> not  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">I</font>,<font color="Olive" title="b1">n</font>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Olive" title="b2">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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="firebrick">::  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  not <font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Olive" title="b1">a</font> holds <br/> not  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">n</font>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Olive" title="b1">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">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="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c7">a</font> implies  not  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">n</font>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c7">a</font> )</span><br/>





<a NAME="E1:8"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
 <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">n</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">n</font>)</span>)</span>,<font color="Maroon" title="c6">n</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T34" title="COMPOS_1:th.34">COMPOS_1:34</a></span>;<br/>
<a NAME="E2:8"/><span class="lab"><font color="Green" title="E4">A2</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c5">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#D19" title="COMPOS_1:def.19">COMPOS_1:def 19</a></span>;<br/>
<a NAME="E3:8"/><span class="lab"><font color="Green" title="E5">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="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">n</font>)</span>)</span>,<font color="Maroon" title="c6">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="c6">n</font></span>)</span> where <font color="Olive" title="b1">m</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="E4:8"/><span class="lab"><font color="Green" title="E6">A4</font></span>: 
 not <font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c7">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">n</font>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c7">a</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">i</font> be   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">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="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">n</font>)</span>)</span> implies  not <font color="Maroon" title="c8">i</font> <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">destroys</a> <font color="Maroon" title="c7">a</font> )</span><br/><span class="kw">assume </span><a NAME="E1:8_1"/>
<font color="Maroon" title="c8">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="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">n</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c8">i</font> <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">destroys</a> <font color="Maroon" title="c7">a</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:8_1"/><span class="lab"><font color="Green" title="E7">A5</font></span>: 
<font color="Maroon" title="c9">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="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">n</font>)</span>)</span>,<font color="Maroon" title="c6">n</font>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:8_1"/><span class="lab"><font color="Green" title="E8">A6</font></span>: 
<font color="Maroon" title="c8">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="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">n</font>)</span>)</span>,<font color="Maroon" title="c6">n</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="funct_1.html#D3" title="FUNCT_1:def.3">FUNCT_1:def 3</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c10">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E6:8_1"/><span class="lab"><font color="Green" title="E9">A7</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c6">n</font>
 <span class="kw">and </span><br/><a NAME="E7:8_1"/><span class="lab"><font color="Green" title="E10">A8</font></span>: 
<font color="Maroon" title="c10">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="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <a class="txt" href="#E3:8_1"><span class="lab"><font color="Green" title="E7">A5</font></span></a></span>;<br/><a NAME="E8:8_1"/><span class="lab"><font color="Green" title="E11">A9</font></span>: 
<font color="Maroon" title="c5">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">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="c5">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="txt" href="#E7:8_1"><span class="lab"><font color="Green" title="E10">A8</font></span></a>, <a class="ref" href="funct_1.html#D3" title="FUNCT_1:def.3">FUNCT_1:def 3</a></span>;<br/><a NAME="E9:8_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">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="c11">ii</font> = <font color="Maroon" title="c5">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font> as   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">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="#E8:8_1"><span class="lab"><font color="Green" title="E11">A9</font></span></a></span>;<br/><a NAME="E11:8_1"/><span class="lab"><font color="Green" title="E12">A10</font></span>: 
 not <font color="Maroon" title="c11">ii</font> <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">destroys</a> <font color="Maroon" title="c7">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E6">A4</font></span></a>, <a class="txt" href="#E8:8_1"><span class="lab"><font color="Green" title="E11">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="c8">i</font> = 
<span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">n</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:8_1"><span class="lab"><font color="Green" title="E8">A6</font></span></a>, <a class="txt" href="#E6:8_1"><span class="lab"><font color="Green" title="E9">A7</font></span></a>, <a class="txt" href="#E7:8_1"><span class="lab"><font color="Green" title="E10">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="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">I</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c6">n</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="txt" href="#E7:8_1"><span class="lab"><font color="Green" title="E10">A8</font></span></a>, <a class="ref" href="compos_1.html#D19" title="COMPOS_1:def.19">COMPOS_1:def 19</a></span>
<br/>.= 
 <a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<font color="Maroon" title="c11">ii</font>,<font color="Maroon" title="c6">n</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="txt" href="#E7:8_1"><span class="lab"><font color="Green" title="E10">A8</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
;<br/><span class="kw">hence </span><a NAME="E13:8_1"/>
 not <font color="Maroon" title="c8">i</font> <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">destroys</a> <font color="Maroon" title="c7">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:8_1"><span class="lab"><font color="Green" title="E12">A10</font></span></a>, <a class="ref" href="scmfsa8a.html#T8" target="_self" title="SCMFSA8A:th.8">Th22</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:8"/>
 not  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">n</font>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c7">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="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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