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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>assume </b><a NAME="E1:21"/><i><font color="Green">E22</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 ;<br/>

<a NAME="E2:21"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:21"/><b>then </b><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a>  or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">c<sub>2</sub></font> )
 </span><b>by </b><i><a class="txt" href="scmbsort.html#E1:21"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scmbsort.html#E3:21"><i><font color="Green">E23</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_1"><b>suppose </b></a><a NAME="E1:21_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">c<sub>3</sub></font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T11">SCMFSA_2:11</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_2"><b>suppose </b></a><a NAME="E1:21_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_2"/>
( <font color="Maroon">c<sub>3</sub></font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">c<sub>3</sub></font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T12">SCMFSA_2:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_3"><b>suppose </b></a><a NAME="E1:21_1_3"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_3"/>
( <font color="Maroon">c<sub>3</sub></font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">c<sub>3</sub></font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T12">SCMFSA_2:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_4"><b>suppose </b></a><a NAME="E1:21_1_4"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_4"/>
( <font color="Maroon">c<sub>3</sub></font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">c<sub>3</sub></font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T11">SCMFSA_2:11</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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