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

<b>let </b><font color="Maroon" title="c1">f</font> be   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">f</font> is <a href="jordan23.html#V2" title="JORDAN23:attr.2">weakly-one-to-one</a> implies for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font> holds <br/><span class="p1">(<span class="default"><a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> )</span><br/>

<b>assume </b><a NAME="E1:42"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c1">f</font> is <a href="jordan23.html#V2" title="JORDAN23:attr.2">weakly-one-to-one</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">p</font>, <font color="Olive" title="b2">q</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font> holds <br/><span class="p1">(<span class="default"><a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font></span><br/>

<b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font> implies <span class="p1">(<span class="default"><a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E2:42"/><i><font color="Green" title="E22">A2</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font>
 <b>and </b><br/><a NAME="E3:42"/><i><font color="Green" title="E23">A3</font></i>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font></span><br/>

<a NAME="E4:42"/><i><font color="Green" title="E24">A4</font></i>: 
 <a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="jordan23.html#T3" target="_self" title="JORDAN23:th.3">Th3</a></i>;<br/>
<a NAME="E5:42"/>
 <a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:42"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="#E2:42"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="#E3:42"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="jordan23.html#T17" target="_self" title="JORDAN23:th.17">Th17</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p2">(<span class="default"><a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_5.html#D3" title="FINSEQ_5:def.3">FINSEQ_5:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="jordan3.html#K5" title="JORDAN3:func.5">B_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
<b>by </b><i><a class="txt" href="#E4:42"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="finseq_5.html#T68" title="FINSEQ_5:th.68">FINSEQ_5:68</a></i>
<br/>.= 
<font color="Maroon" title="c3">q</font>
<b>by </b><i><a class="txt" href="#E1:42"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="#E2:42"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="#E3:42"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="jordan23.html#T19" target="_self" title="JORDAN23:th.19">Th19</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
