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

<span class="kw">let </span><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <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">C</font> being   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>   non  <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a>   non  <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>  holds <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Olive" title="b1">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Olive" title="b1">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">N-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Olive" title="b1">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Olive" title="b1">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">C</font> be   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>   non  <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a>   non  <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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"> <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">N-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">Wmi</font> =  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">Nmi</font> =  <a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">N-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">Nma</font> =  <a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">N-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">Ema</font> =  <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">Rot</font> =  <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span>);<br/>
<a NAME="E1:25"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="revrot_1.html#T33" title="REVROT_1:th.33">REVROT_1:33</a></span>;<br/>
<a NAME="E2:25"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A2</font></span>: 
 <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_2.html#T46" title="SPRECT_2:th.46">SPRECT_2:46</a></span>;<br/>
<a NAME="E3:25"/>
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_2.html#T43" title="SPRECT_2:th.43">SPRECT_2:43</a></span>;<br/>
<a NAME="E4:25"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_6.html#T92" title="FINSEQ_6:th.92">FINSEQ_6:92</a></span>;<br/>
<a NAME="E5:25"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A3</font></span>: 
( <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">N-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">N-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="sprect_5.html#T24" title="SPRECT_5:th.24">SPRECT_5:24</a>, <a class="ref" href="sprect_5.html#T25" title="SPRECT_5:th.25">SPRECT_5:25</a></span>;<br/>
<a NAME="E6:25"/><span class="lab"><font color="Green" title="E22">A4</font></span>: 
 <a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">N-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="sprect_2.html#T40" title="SPRECT_2:th.40">SPRECT_2:40</a></span>;<br/>
<a NAME="E7:25"/>
 <a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">N-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="sprect_2.html#T39" title="SPRECT_2:th.39">SPRECT_2:39</a></span>;<br/>
<a NAME="E8:25"/><span class="kw">then </span>
(  <a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p5">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<span class="p2">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:25"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E5:25"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="jordan1e.html#D1" title="JORDAN1E:def.1">JORDAN1E:def 1</a>, <a class="ref" href="sprect_5.html#T3" title="SPRECT_5:th.3">SPRECT_5:3</a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:25"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">N-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">..</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c1">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:25"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E5:25"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E6:25"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="sprect_5.html#T3" title="SPRECT_5:th.3">SPRECT_5:3</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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