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<span class="kw">let </span><font color="Maroon" title="c1">f</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="Maroon" title="c1">f</font> is  <a href="jordan23.html#V1" title="JORDAN23:attr.1">almost-one-to-one</a>  &amp; <font color="Maroon" title="c1">f</font> is  <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  &amp; <font color="Maroon" title="c1">f</font> is  <a href="topreal1.html#V2" title="TOPREAL1:attr.2">unfolded</a>  &amp; <font color="Maroon" title="c1">f</font> is  <a href="topreal1.html#V3" title="TOPREAL1:attr.3">s.n.c.</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">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#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">q</font> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 holds <br/> <a href="jordan3.html#K4" title="JORDAN3:func.4">B_Cut</a> (<font color="Maroon" title="c1">f</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>) is  <a href="topreal1.html#V4" title="TOPREAL1:attr.4">being_S-Seq</a> </span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">f</font> is  <a href="jordan23.html#V1" title="JORDAN23:attr.1">almost-one-to-one</a>  &amp; <font color="Maroon" title="c1">f</font> is  <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  &amp; <font color="Maroon" title="c1">f</font> is  <a href="topreal1.html#V2" title="TOPREAL1:attr.2">unfolded</a>  &amp; <font color="Maroon" title="c1">f</font> is  <a href="topreal1.html#V3" title="TOPREAL1:attr.3">s.n.c.</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">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#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font> &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">q</font> &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 implies  <a href="jordan3.html#K4" title="JORDAN3:func.4">B_Cut</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>) is  <a href="topreal1.html#V4" title="TOPREAL1:attr.4">being_S-Seq</a>  )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:67"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
( <font color="Maroon" title="c1">f</font> is  <a href="jordan23.html#V1" title="JORDAN23:attr.1">almost-one-to-one</a>  &amp; <font color="Maroon" title="c1">f</font> is  <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  &amp; <font color="Maroon" title="c1">f</font> is  <a href="topreal1.html#V2" title="TOPREAL1:attr.2">unfolded</a>  &amp; <font color="Maroon" title="c1">f</font> is  <a href="topreal1.html#V3" title="TOPREAL1:attr.3">s.n.c.</a>  )
 <span class="kw">and </span><br/><a NAME="E2:67"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2
 <span class="kw">and </span><br/><a NAME="E3:67"/><span class="lab"><font color="Green" title="E39">A3</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font>
 <span class="kw">and </span><br/><a NAME="E4:67"/><span class="lab"><font color="Green" title="E40">A4</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font>
 <span class="kw">and </span><br/><a NAME="E5:67"/><span class="lab"><font color="Green" title="E41">A5</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">q</font>
 <span class="kw">and </span><br/><a NAME="E6:67"/><span class="lab"><font color="Green" title="E42">A6</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <span class="kw">and </span><br/><a NAME="E7:67"/><span class="lab"><font color="Green" title="E43">A7</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="jordan3.html#K4" title="JORDAN3:func.4">B_Cut</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>) is  <a href="topreal1.html#V4" title="TOPREAL1:attr.4">being_S-Seq</a> </span><br/>

<a NAME="E8:67"/>
 <a href="jordan3.html#K4" title="JORDAN3:func.4">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="jordan3.html#R1" title="JORDAN3:pred.1">is_S-Seq_joining</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E41">A5</font></span></a>, <a class="txt" href="#E6:67"><span class="lab"><font color="Green" title="E42">A6</font></span></a>, <a class="txt" href="#E7:67"><span class="lab"><font color="Green" title="E43">A7</font></span></a>, <a class="ref" href="jordan23.html#T43" target="_self" title="JORDAN23:th.43">Th43</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:67"/>
 <a href="jordan3.html#K4" title="JORDAN3:func.4">B_Cut</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>) is  <a href="topreal1.html#V4" title="TOPREAL1:attr.4">being_S-Seq</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="jordan3.html#D2" title="JORDAN3:def.2">JORDAN3:def 2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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