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<b>let </b><font color="Maroon" title="c1">fl</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">  ex <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  st <font color="Maroon" title="c1">fl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> <font color="Olive" title="b1">i</font></span><br/>

<a NAME="E1:7"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c1">fl</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> 
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#D5" target="_self" title="SCMFSA_2:def.5">Def5</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c2">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:7"/><i><font color="Green" title="E7">A2</font></i>: 
( <font color="Maroon" title="c1">fl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font> or <font color="Maroon" title="c1">fl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">k</font> )
 <b>by </b><i><a class="ref" href="int_1.html#D1" title="INT_1:def.1">INT_1:def 1</a></i>;<br/>
<a NAME="E4:7"/>
<font color="Maroon" title="c2">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E1:7"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="scmfsa_2.html#E3:7"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E6:7"/><i><font color="Green" title="E8">A3</font></i>: 
<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T6" title="NAT_1:th.6">NAT_1:6</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">i</font> = <font color="Maroon" title="c3">i</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">i</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">fl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> <font color="Maroon" title="c4">i</font></span><br/>

<b>thus </b><a NAME="E8:7"/>
<font color="Maroon" title="c1">fl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E1:7"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="scmfsa_2.html#E3:7"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="scmfsa_2.html#E6:7"><i><font color="Green" title="E8">A3</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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