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<span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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> 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; <font color="Olive" title="b1">p</font> <a href="tarski.html#R2" title="TARSKI: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="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 holds <br/> <a href="jordan3.html#K3" title="JORDAN3:func.3">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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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; <font color="Maroon" title="c2">p</font> <a href="tarski.html#R2" title="TARSKI: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="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 implies  <a href="jordan3.html#K3" title="JORDAN3:func.3">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/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:60"/><span class="lab"><font color="Green" title="E31">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="E2:60"/><span class="lab"><font color="Green" title="E32">A2</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="tarski.html#R2" title="TARSKI: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="E3:60"/><span class="lab"><font color="Green" title="E33">A3</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
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="jordan3.html#K3" title="JORDAN3:func.3">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="E4:60"/>
 <a href="jordan3.html#K3" title="JORDAN3:func.3">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="finseq_6.html#K3" title="FINSEQ_6:func.3">mid</a> (<font color="Maroon" title="c1">f</font>,1,<span class="p2">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">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="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:60"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="jordan3.html#D4" onmouseover="rs('jordan3/D4')" onmouseout="rh()">JORDAN3:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:60"/>
 <a href="jordan3.html#K3" title="JORDAN3:func.3">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="txt" href="#E3:60"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="jordan23.html#T35" target="_self" onmouseover="rs('jordan23/T35')" onmouseout="rh()">Th35</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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