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<b>let </b><font color="Maroon" title="c1">t</font> be   <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</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"> for <font color="Olive" title="b1">p</font> being  <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <br/> for <font color="Olive" title="b2">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a>  &amp; <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">t</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Olive" title="b1">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Olive" title="b1">p</font></span>)</span> &amp; <font color="Olive" title="b2">x</font> is  not    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  holds <br/><font color="Olive" title="b2">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> </span><br/><b>let </b><font color="Maroon" title="c2">p</font> be   <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</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"> for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a>  &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">t</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c2">p</font></span>)</span> &amp; <font color="Olive" title="b1">x</font> is  not    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  holds <br/><font color="Olive" title="b1">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> </span><br/><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a>  &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">t</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c2">p</font></span>)</span> &amp; <font color="Maroon" title="c3">x</font> is  not    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  implies <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  )</span><br/>





<b>set </b><font color="Maroon" title="c4">D1</font> =  <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Maroon" title="c2">p</font>;<br/>
<b>set </b><font color="Maroon" title="c5">D2</font> =  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c2">p</font>;<br/>
<b>assume </b><a NAME="E1:13"/><i><font color="Green" title="E14">A1</font></i>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a>  &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">t</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c2">p</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  or <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  )</span><br/>

<a NAME="E2:13"/><b>then </b>
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">t</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Maroon" title="c2">p</font></span>)</span> or <font color="Maroon" title="c3">x</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> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:13"/><b>then </b><i><font color="Green" title="E15">A2</font></i>: 
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">t</font> or <font color="Maroon" title="c3">x</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="c2">p</font> or <font color="Maroon" title="c3">x</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> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:13_1"/>
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  or <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a>  or <font color="Maroon" title="c3">x</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="c2">p</font> or <font color="Maroon" title="c3">x</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><b>by </b><i><a class="txt" href="scmbsort.html#E1:13"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="scmbsort.html#E3:13"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1"><b>suppose </b></a><a NAME="E1:13_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  or <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  )</span><br/><div class="add"><b>hence </b><a NAME="E2:13_1_1"/>
( <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  or <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T11" title="SCMFSA_2:th.11">SCMFSA_2:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_2"><b>suppose </b></a><a NAME="E1:13_1_2"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  or <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  )</span><br/><div class="add"><b>hence </b><a NAME="E2:13_1_2"/>
( <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  or <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T12" title="SCMFSA_2:th.12">SCMFSA_2:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_3"><b>suppose </b></a><a NAME="E1:13_1_3"/>
<font color="Maroon" title="c3">x</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="c2">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  or <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  )</span><br/><div class="add"><b>hence </b><a NAME="E2:13_1_3"/>
( <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  or <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T12" title="SCMFSA_2:th.12">SCMFSA_2:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_4"><b>suppose </b></a><a NAME="E1:13_1_4"/>
<font color="Maroon" title="c3">x</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  or <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  )</span><br/><div class="add"><b>hence </b><a NAME="E2:13_1_4"/>
( <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  or <font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T11" title="SCMFSA_2:th.11">SCMFSA_2:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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