<?xml version="1.0"?>
<div class="add">

<b>let </b><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:()"><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>  holds  <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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</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></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"> <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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</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><br/>





<b>set </b><font color="Maroon" title="c4">a</font> = <font color="Maroon" title="c1">aa</font>;<br/>
<b>set </b><font color="Maroon" title="c5">b</font> = <font color="Maroon" title="c2">bb</font>;<br/>
<b>set </b><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/>
<b>set </b><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/>
<b>set </b><font color="Maroon" title="c8">i0</font> = <span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p2"><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#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font>;<br/>
<b>set </b><font color="Maroon" title="c9">i1</font> = <span class="p1">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p2"><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#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">bb</font>;<br/>
<b>set </b><font color="Maroon" title="c10">i2</font> = <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <span class="p1">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p2"><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>;<br/>
<b>set </b><font color="Maroon" title="c11">i3</font> = <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">bb</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p2"><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>;<br/>
<i><font color="Green" title="E37">A1</font></i>:  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</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#K2" title="SF_MASTR:func.2">UsedIntLoc</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#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</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#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">bb</font></span>)</span></span>)</span> <a href="scmfsa6a.html#K7" title="SCMFSA6A:func.7">';'</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#K16" title="SCMFSA_2:func.16">:=</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#K1" title="SF_MASTR:func.1">UsedIntLoc</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#K16" title="SCMFSA_2:func.16">:=</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>
<b>by </b><i><a class="ref" href="sf_mastr.html#T34" title="SF_MASTR:th.34">SF_MASTR:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</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#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</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#K15" title="SCMFSA_2:func.15">:=</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#K1" title="SF_MASTR:func.1">UsedIntLoc</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#K16" title="SCMFSA_2:func.16">:=</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#K1" title="SF_MASTR:func.1">UsedIntLoc</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#K16" title="SCMFSA_2:func.16">:=</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>
<b>by </b><i><a class="ref" href="sf_mastr.html#T34" title="SF_MASTR:th.34">SF_MASTR:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sf_mastr.html#K1" title="SF_MASTR:func.1">UsedIntLoc</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#K15" title="SCMFSA_2:func.15">:=</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#K1" title="SF_MASTR:func.1">UsedIntLoc</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#K15" title="SCMFSA_2:func.15">:=</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#K1" title="SF_MASTR:func.1">UsedIntLoc</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#K16" title="SCMFSA_2:func.16">:=</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#K1" title="SF_MASTR:func.1">UsedIntLoc</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#K16" title="SCMFSA_2:func.16">:=</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>
<b>by </b><i><a class="ref" href="sf_mastr.html#T35" title="SF_MASTR:th.35">SF_MASTR:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</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>,<font color="Maroon" title="c1">aa</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</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#K1" title="SF_MASTR:func.1">UsedIntLoc</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#K15" title="SCMFSA_2:func.15">:=</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#K1" title="SF_MASTR:func.1">UsedIntLoc</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#K16" title="SCMFSA_2:func.16">:=</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#K1" title="SF_MASTR:func.1">UsedIntLoc</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#K16" title="SCMFSA_2:func.16">:=</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>
<b>by </b><i><a class="ref" href="sf_mastr.html#T21" title="SF_MASTR:th.21">SF_MASTR:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</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>,<font color="Maroon" title="c1">aa</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><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>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></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#K1" title="SF_MASTR:func.1">UsedIntLoc</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#K16" title="SCMFSA_2:func.16">:=</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#K1" title="SF_MASTR:func.1">UsedIntLoc</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#K16" title="SCMFSA_2:func.16">:=</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>
<b>by </b><i><a class="ref" href="sf_mastr.html#T21" title="SF_MASTR:th.21">SF_MASTR:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</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>,<font color="Maroon" title="c1">aa</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><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>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><span class="p3">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</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>,<font color="Maroon" title="c1">aa</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></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#K1" title="SF_MASTR:func.1">UsedIntLoc</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#K16" title="SCMFSA_2:func.16">:=</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>
<b>by </b><i><a class="ref" href="sf_mastr.html#T21" title="SF_MASTR:th.21">SF_MASTR:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</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>,<font color="Maroon" title="c1">aa</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><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>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><span class="p3">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</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>,<font color="Maroon" title="c1">aa</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p3"><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>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span>
<b>by </b><i><a class="ref" href="sf_mastr.html#T21" title="SF_MASTR:th.21">SF_MASTR:21</a></i>
;<br/>
<b>let </b><font color="Maroon" title="c12">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> or <font color="Maroon" title="c12">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> <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><br/>

<b>assume </b><a NAME="E2:45"/><i><font color="Green" title="E38">A2</font></i>: 
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c12">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> <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><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_2"/>
( <font color="Maroon" title="c12">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">aa</font> or <font color="Maroon" title="c12">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">bb</font> )
 </span><b>by </b><i><a class="txt" href="#E2:45"><i><font color="Green" title="E38">A2</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1"><b>suppose </b></a><a NAME="E1:45_2_1"/>
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">aa</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c12">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> <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><br/><div class="add"><a NAME="E2:45_2_1"/><b>then </b>
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><span class="p2">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p3"><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>,<font color="Maroon" title="c1">aa</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E3:45_2_1"/><b>then </b>
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><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>,<font color="Maroon" title="c1">aa</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><span class="p3">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</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>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><span class="p2">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p3"><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>,<font color="Maroon" title="c1">aa</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E4:45_2_1"/>
<font color="Maroon" title="c12">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> <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>
 <b>by </b><i><a class="txt" href="#E1:45"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</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="45_2_2"><b>suppose </b></a><a NAME="E1:45_2_2"/>
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">bb</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c12">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> <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><br/><div class="add"><a NAME="E2:45_2_2"/><b>then </b>
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p3"><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>,<font color="Maroon" title="c2">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E3:45_2_2"/>
<font color="Maroon" title="c12">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> <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>
 <b>by </b><i><a class="txt" href="#E1:45"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</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>

</div>
