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<b>let </b><font color="Maroon" title="c1">b</font>, <font color="Maroon" title="c2">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:()"><i><font color="Red">::  thesis: </font></i></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">b</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c2">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> or <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c1">b</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#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/><b>let </b><font color="Maroon" title="c3">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:()"><i><font color="Red">::  thesis: </font></i></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">b</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">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> or <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c1">b</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#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="c3">f</font></span><br/><b>let </b><font color="Maroon" title="c4">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c1">b</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">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="c4">p</font> or <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c1">b</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="c4">p</font> ) implies  <a href="sf_mastr.html#K8" title="SF_MASTR:func.8">First*NotUsed</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">f</font> )</span><br/>







<b>assume </b><a NAME="E1:75"/>
( <font color="Maroon" title="c1">b</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">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="c4">p</font> or <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c1">b</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="c4">p</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="sf_mastr.html#K8" title="SF_MASTR:func.8">First*NotUsed</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">f</font></span><br/>

<b>then consider </b><font color="Maroon" title="c5">i</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:75"/><i><font color="Green" title="E52">A1</font></i>: 
( <font color="Maroon" title="c5">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="c4">p</font> &amp; ( <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">b</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">a</font> or <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c1">b</font> ) )
 ;<br/>
<a NAME="E4:75"/>
 <a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <font color="Maroon" title="c5">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="c3">f</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:75"><i><font color="Green" title="E52">A1</font></i></a>, <a class="ref" href="sf_mastr.html#T37" target="_self" title="SF_MASTR:th.37">Th37</a></i>;<br/>
<a NAME="E5:75"/><b>then </b>
( <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">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="c4">p</font> &amp; not  <a href="sf_mastr.html#K8" title="SF_MASTR:func.8">First*NotUsed</a> <font color="Maroon" title="c4">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="c4">p</font> )
 
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:75"><i><font color="Green" title="E52">A1</font></i></a>, <a class="ref" href="sf_mastr.html#T39" target="_self" title="SF_MASTR:th.39">Th39</a>, <a class="ref" href="sf_mastr.html#T61" target="_self" title="SF_MASTR:th.61">Th61</a></i>;<br/>
<b>hence </b><a NAME="E6:75"/>
 <a href="sf_mastr.html#K8" title="SF_MASTR:func.8">First*NotUsed</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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