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<b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:58"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">f</font> is <a href="jordan23.html#V3" target="_self">poorly-one-to-one</a> &amp; <font color="Maroon">f</font> is <a href="topreal1.html#V2">unfolded</a> &amp; <font color="Maroon">f</font> is <a href="topreal1.html#V3">s.n.c.</a> )
 <b>and </b><br/><a NAME="E2:58"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E3:58"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>and </b><br/><a NAME="E4:58"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span>
 ;<br/>

<a NAME="E5:58"/><i><font color="Green">E48</font></i>: 
 <a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font> is <a href="jordan23.html#V3" target="_self">poorly-one-to-one</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:58"/><i><font color="Green">E49</font></i>: 
 <a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font> is <a href="topreal1.html#V2">unfolded</a>
 
<b>by </b><i>, <a class="ref" href="sppol_2.html#T29">SPPOL_2:29</a></i>;<br/>
<a NAME="E7:58"/><i><font color="Green">E50</font></i>: 
 <a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font> is <a href="topreal1.html#V3">s.n.c.</a>
 
<b>by </b><i>, <a class="ref" href="sppol_2.html#T36">SPPOL_2:36</a></i>;<br/>
<a NAME="E8:58"/><i><font color="Green">E51</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>;<br/>
<a NAME="E9:58"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E10:58"/><b>then </b><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/>
<a NAME="E11:58"/>
 <a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="jordan23.html#T1" target="_self">Th1</a>, <a class="ref" href="jordan3.html#T41">JORDAN3:41</a></i>;<br/>
<a NAME="E12:58"/><b>then </b><i><font color="Green">E53</font></i>: 
<span class="p1">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E13:58"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E14:58"/><b>then </b>
<span class="p1">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E15:58"/><b>then </b><i><font color="Green">E58</font></i>: 
<span class="p1">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_5.html#T60">FINSEQ_5:60</a></i>;<br/>
<a NAME="E16:58"/>
<span class="p1">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i>, , , <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>
<a NAME="E17:58"/><b>then </b><i><font color="Green">E62</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/>
<a NAME="E18:58"/>
 <a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="jordan23.html#T1" target="_self">Th1</a>, <a class="ref" href="jordan3.html#T41">JORDAN3:41</a></i>;<br/>
<a NAME="E19:58"/><b>then </b><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<font color="Maroon">p</font> = 
<span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_6.html#T29">FINSEQ_6:29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_5.html#T61">FINSEQ_5:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>
;<br/>
<a NAME="E21:58"/><b>then </b><i><font color="Green">E64</font></i>: 
<span class="p1">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<span class="p2">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan23.html#E1:58"><i><font color="Green">E35</font></i></a>, <a class="ref" href="jordan23.html#T3" target="_self">Th3</a>, , <a class="ref" href="jordan23.html#D1" target="_self">Def1</a>, <a class="ref" href="jordan23.html#D2" target="_self">Def2</a>, <a class="ref" href="jordan23.html#D3" target="_self">Def3</a>, </i>;<br/>
<b>thus </b><a NAME="E22:58"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<span class="p3">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="jordan23.html#D3" target="_self">Def3</a>, </i>;<br/>


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