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<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="firebrick">::  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="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>  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="relset_1.html#K2" title="RELSET_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="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b2">p</font> ) holds <br/> <a href="sf_mastr.html#K8" title="SF_MASTR:func.8">First*NotUsed</a> <font color="Olive" title="b2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">f</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font> being   <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>  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="relset_1.html#K2" title="RELSET_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="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b1">p</font> ) holds <br/> <a href="sf_mastr.html#K8" title="SF_MASTR:func.8">First*NotUsed</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">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"> ( ( <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="relset_1.html#K2" title="RELSET_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="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c3">p</font> ) implies  <a href="sf_mastr.html#K8" title="SF_MASTR:func.8">First*NotUsed</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">f</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:75"/>
( <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="relset_1.html#K2" title="RELSET_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="relset_1.html#K2" title="RELSET_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="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="sf_mastr.html#K8" title="SF_MASTR:func.8">First*NotUsed</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">f</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">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><span class="kw"> such that </span><br/><a NAME="E3:75"/><span class="lab"><font color="Green" title="E52">A1</font></span>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c3">p</font>
 <span class="kw">and </span><br/><a NAME="E4:75"/><span class="lab"><font color="Green" title="E53">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="E5:75"/>
 <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> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">f</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="#E4:75"><span class="lab"><font color="Green" title="E53">A2</font></span></a>, <a class="ref" href="sf_mastr.html#T34" target="_self" title="SF_MASTR:th.34">Th38</a></span>;<br/>
<a NAME="E6:75"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A3</font></span>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">f</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#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Maroon" title="c3">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:75"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="ref" href="sf_mastr.html#T35" target="_self" title="SF_MASTR:th.35">Th39</a></span>;<br/>
<a NAME="E7:75"/>
 not  <a href="sf_mastr.html#K8" title="SF_MASTR:func.8">First*NotUsed</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Maroon" title="c3">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T57" target="_self" title="SF_MASTR:th.57">Th61</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:75"/>
 <a href="sf_mastr.html#K8" title="SF_MASTR:func.8">First*NotUsed</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:75"><span class="lab"><font color="Green" title="E54">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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