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<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</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">  for <font color="Olive" title="b1">l</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">i</font> being   <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>  st ( <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> or <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c2">b</font> or <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">l</font> or <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">l</font> or <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">l</font> ) holds <br/> <a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">l</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">i</font> being   <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>  st ( <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> or <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c2">b</font> or <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c3">l</font> or <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c3">l</font> or <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c3">l</font> ) holds <br/> <a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">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="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c2">b</font> or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c3">l</font> or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c3">l</font> or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c3">l</font> ) implies  <a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>







<span class="kw">assume </span><a NAME="E1:37"/>
( <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c2">b</font> or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c3">l</font> or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c3">l</font> or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c3">l</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<a NAME="E2:37"/><span class="kw">then </span>
(  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T18" title="SCMFSA_2:th.18">SCMFSA_2:18</a>, <a class="ref" href="scmfsa_2.html#T19" title="SCMFSA_2:th.19">SCMFSA_2:19</a>, <a class="ref" href="scmfsa_2.html#T20" title="SCMFSA_2:th.20">SCMFSA_2:20</a>, <a class="ref" href="scmfsa_2.html#T21" title="SCMFSA_2:th.21">SCMFSA_2:21</a>, <a class="ref" href="scmfsa_2.html#T22" title="SCMFSA_2:th.22">SCMFSA_2:22</a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:37"/>
 <a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#D3" target="_self" title="SF_MASTR:def.3">Def3</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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