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<span class="kw">let </span><font color="Maroon" title="c1">dl</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"> <font color="Maroon" title="c1">dl</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span><br/>

<a NAME="E1:79"/>
<font color="Maroon" title="c1">dl</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#D5" target="_self" title="SCMFSA_2:def.5">Def5</a></span>;<br/>
<a NAME="E2:79"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A</font></span>: 
<font color="Maroon" title="c1">dl</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
 
;<br/>
<a NAME="E3:79"/><span class="lab"><font color="Green" title="E42">B</font></span>: 
 <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="numbers.html#D4" title="NUMBERS:def.4">NUMBERS:def 4</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:79_1"/>
 <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:79_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">pc</font></span>: 
 <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:79"><span class="lab"><font color="Green" title="E42">B</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="79_1_1"><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="E1:79_1_1"/>
(  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  or  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79_1"><span class="lab"><font color="Green" title="E43">pc</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="79_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:79_1_1_1"/>
 <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:79_1_1_1"/>
contradiction
 ; <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="79_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:79_1_1_2"/>
 <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1: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"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:79_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finset_1.html#T34" title="FINSET_1:th.34">FINSET_1:34</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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:79"/>
<font color="Maroon" title="c1">dl</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E41">A</font></span></a>, <a class="ref" href="scmfsa_2.html#T7" target="_self" title="SCMFSA_2:th.7">Th7</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/>


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