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<span class="kw">let </span><font color="Maroon" title="c2">p</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">ic</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><br/>  for <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <br/>  for <font color="Olive" title="b3">la</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>   st <font color="Olive" title="b1">ic</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="c2">p</font> &amp; ( <font color="Olive" title="b1">ic</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b3">la</font> or <font color="Olive" title="b1">ic</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b3">la</font> ) holds <br/><font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c2">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">ic</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">  for <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <br/>  for <font color="Olive" title="b2">la</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>   st <font color="Maroon" title="c3">ic</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="c2">p</font> &amp; ( <font color="Maroon" title="c3">ic</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b2">la</font> or <font color="Maroon" title="c3">ic</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b2">la</font> ) holds <br/><font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c2">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">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">  for <font color="Olive" title="b1">la</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>   st <font color="Maroon" title="c3">ic</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="c2">p</font> &amp; ( <font color="Maroon" title="c3">ic</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">la</font> or <font color="Maroon" title="c3">ic</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">la</font> ) holds <br/><font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c2">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">la</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"> ( <font color="Maroon" title="c3">ic</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="c2">p</font> &amp; ( <font color="Maroon" title="c3">ic</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c5">la</font> or <font color="Maroon" title="c3">ic</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c5">la</font> ) implies <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c2">p</font> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:8"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
<font color="Maroon" title="c3">ic</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="c2">p</font>
 <span class="kw">and </span><br/><a NAME="E2:8"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
( <font color="Maroon" title="c3">ic</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c5">la</font> or <font color="Maroon" title="c3">ic</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c5">la</font> )
 ; <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">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c2">p</font></span><br/>

<a NAME="E3:8"/><span class="lab"><font color="Green" title="E11">A3</font></span>: 
 <a href="sf_mastr.html#K1" title="SF_MASTR:func.1">UsedIntLoc</a> <font color="Maroon" title="c3">ic</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">a</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="sf_mastr.html#T16" title="SF_MASTR:th.16">SF_MASTR:16</a></span>;<br/>
<a NAME="E4:8"/>
 <a href="sf_mastr.html#K1" title="SF_MASTR:func.1">UsedIntLoc</a> <font color="Maroon" title="c3">ic</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="sf_mastr.html#T19" title="SF_MASTR:th.19">SF_MASTR:19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:8"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#T31" title="ZFMISC_1:th.31">ZFMISC_1:31</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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