<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">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"> for <font color="Olive" title="b1">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <br/> for <font color="Olive" title="b2">p</font> being  <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>   st ( <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b1">f</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="Olive" title="b2">p</font> or <font color="Olive" title="b1">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c1">a</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="Olive" title="b2">p</font> ) holds <br/> <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <font color="Olive" title="b2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</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">p</font> being  <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>   st ( <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Maroon" title="c2">f</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="Olive" title="b1">p</font> or <font color="Maroon" title="c2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c1">a</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="Olive" title="b1">p</font> ) holds <br/> <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</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"> ( ( <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Maroon" title="c2">f</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">p</font> or <font color="Maroon" title="c2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c1">a</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">p</font> ) implies  <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">a</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:73"/>
( <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Maroon" title="c2">f</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">p</font> or <font color="Maroon" title="c2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c1">a</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">p</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">a</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">i</font> being   <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"> such that </span><br/><a NAME="E3:73"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
<font color="Maroon" title="c4">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> <font color="Maroon" title="c3">p</font>
 <span class="kw">and </span><br/><a NAME="E4:73"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
( <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#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Maroon" title="c2">f</font> or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c1">a</font> )
 ;<br/>
<a NAME="E5:73"/>
 <a href="sf_mastr.html#K1" title="SF_MASTR:func.1">UsedIntLoc</a> <font color="Maroon" title="c4">i</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="c1">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="#E4:73"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="sf_mastr.html#T22" target="_self" title="SF_MASTR:th.22">Th22</a></span>;<br/>
<a NAME="E6:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A3</font></span>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">a</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <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="c3">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="sf_mastr.html#T23" target="_self" title="SF_MASTR:th.23">Th23</a></span>;<br/>
<a NAME="E7:73"/>
not  <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <font color="Maroon" title="c3">p</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="c3">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T54" target="_self" title="SF_MASTR:th.54">Th54</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:73"/>
 <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:73"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</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>
