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<span class="kw">let </span><font color="Maroon" title="c1">aa</font>, <font color="Maroon" title="c2">bb</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>  holds   <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K4" title="SFMASTR3:func.4">swap</a> (<font color="Olive" title="b1">f</font>,<font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font>)</span>)</span> <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="Olive" title="b1">f</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K4" title="SFMASTR3:func.4">swap</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font>)</span>)</span> <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></span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">a</font> = <font color="Maroon" title="c1">aa</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">b</font> = <font color="Maroon" title="c2">bb</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">aux1</font> = 1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">aux2</font> = 2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span>;<br/>
<span class="kw">thus </span> <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K4" title="SFMASTR3:func.4">swap</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font>)</span>)</span> <a href="scmfsa6a.html#K7" title="SCMFSA6A:func.7">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">bb</font>)</span>)</span></span>)</span> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p4">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p5"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span></span>)</span></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#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">bb</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p4"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T46" title="SF_MASTR:th.46">SF_MASTR:46</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font>)</span>)</span> <a href="scmfsa6a.html#K7" title="SCMFSA6A:func.7">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">bb</font>)</span>)</span></span>)</span> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p4">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p5"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T33" title="SF_MASTR:th.33">SF_MASTR:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font>)</span>)</span> <a href="scmfsa6a.html#K7" title="SCMFSA6A:func.7">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">bb</font>)</span>)</span></span>)</span></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#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p4">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p5"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T46" title="SF_MASTR:th.46">SF_MASTR:46</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font>)</span>)</span> <a href="scmfsa6a.html#K7" title="SCMFSA6A:func.7">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">bb</font>)</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><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></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T33" title="SF_MASTR:th.33">SF_MASTR:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font>)</span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">bb</font>)</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><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></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T47" title="SF_MASTR:th.47">SF_MASTR:47</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><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="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p0"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c1">aa</font>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">bb</font>)</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><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></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T33" title="SF_MASTR:th.33">SF_MASTR:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><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="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><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></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T33" title="SF_MASTR:th.33">SF_MASTR:33</a></span>
<br/>.= 
<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 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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