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<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"> for <font color="Olive" title="b1">p</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="topreal1.html#V4" title="TOPREAL1:attr.4">being_S-Seq</a> &amp; <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="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 holds <br/> <a href="jordan3.html#K4" title="JORDAN3:func.4">R_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Olive" title="b1">p</font> <a href="jordan3.html#R1" title="JORDAN3:pred.1">is_S-Seq_joining</a> <font color="Maroon" title="c1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1,<font color="Olive" title="b1">p</font></span><br/><b>let </b><font color="Maroon" title="c2">p</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="c1">f</font> is <a href="topreal1.html#V4" title="TOPREAL1:attr.4">being_S-Seq</a> &amp; <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="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 implies  <a href="jordan3.html#K4" title="JORDAN3:func.4">R_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">p</font> <a href="jordan3.html#R1" title="JORDAN3:pred.1">is_S-Seq_joining</a> <font color="Maroon" title="c1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1,<font color="Maroon" title="c2">p</font> )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:56"/><i><font color="Green" title="E49">A1</font></i>: 
<font color="Maroon" title="c1">f</font> is <a href="topreal1.html#V4" title="TOPREAL1:attr.4">being_S-Seq</a>
 <b>and </b><br/><a NAME="E2:56"/><i><font color="Green" title="E50">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="E3:56"/><i><font color="Green" title="E51">A3</font></i>: 
<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
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="jordan3.html#K4" title="JORDAN3:func.4">R_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">p</font> <a href="jordan3.html#R1" title="JORDAN3:pred.1">is_S-Seq_joining</a> <font color="Maroon" title="c1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1,<font color="Maroon" title="c2">p</font></span><br/>

<a NAME="E4:56"/>
 <a href="jordan3.html#K4" title="JORDAN3:func.4">R_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c1">f</font>,1,<span class="p2">(<span class="default"><a href="jordan3.html#K2" title="JORDAN3:func.2">Index</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="#E3:56"><i><font color="Green" title="E51">A3</font></i></a>, <a class="ref" href="jordan3.html#D5" target="_self" title="JORDAN3:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E5:56"/>
 <a href="jordan3.html#K4" title="JORDAN3:func.4">R_Cut</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">p</font> <a href="jordan3.html#R1" title="JORDAN3:pred.1">is_S-Seq_joining</a> <font color="Maroon" title="c1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1,<font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="#E1:56"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="#E2:56"><i><font color="Green" title="E50">A2</font></i></a>, <a class="txt" href="#E3:56"><i><font color="Green" title="E51">A3</font></i></a>, <a class="ref" href="jordan3.html#T52" target="_self" title="JORDAN3:th.52">Th52</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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