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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="Red">::  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  <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/><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="Red">::  thesis: </font></span></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/>





<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">set </span><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#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">aa</font>;<br/>
<span class="kw">set </span><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#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">bb</font>;<br/>
<span class="kw">set </span><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#K15" title="SCMFSA_2:func.15">:=</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/>
<span class="kw">set </span><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#K15" title="SCMFSA_2:func.15">:=</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/>
<span class="lab"><font color="Green" title="E37">A1</font></span>:  <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#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#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#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#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#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#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#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#T34" title="SF_MASTR:th.34">SF_MASTR:34</a></span>
<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#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#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#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#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#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#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#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#T34" title="SF_MASTR:th.34">SF_MASTR:34</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#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#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#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#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#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#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#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#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#T35" title="SF_MASTR:th.35">SF_MASTR:35</a></span>
<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#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#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#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#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#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#T21" title="SF_MASTR:th.21">SF_MASTR:21</a></span>
<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#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#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#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#T21" title="SF_MASTR:th.21">SF_MASTR:21</a></span>
<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#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#T21" title="SF_MASTR:th.21">SF_MASTR:21</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T21" title="SF_MASTR:th.21">SF_MASTR:21</a></span>
;<br/>
<span class="kw">let </span><font color="Maroon" title="c12">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E2:51"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="51_2"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:51_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><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:51"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_2_1"><span class="kw">suppose </span></a><a NAME="E1:51_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E2:51_2_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><a NAME="E3:51_2_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E4:51_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_2_2"><span class="kw">suppose </span></a><a NAME="E1:51_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E2:51_2_2"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:51_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
