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<span class="kw">let </span><font color="Maroon" title="c1">p1</font>, <font color="Maroon" title="c2">p2</font>, <font color="Maroon" title="c3">p3</font>, <font color="Maroon" title="c4">p4</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">  for <font color="Olive" title="b1">P</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</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>  st <font color="Olive" title="b1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b2">p</font> where <font color="Olive" title="b2">p</font> is   <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> : <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><font color="Olive" title="b2">p</font></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 </span> } </span>  &amp; <font color="Maroon" title="c4">p4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Olive" title="b1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Olive" title="b1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>,<font color="Olive" title="b1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c4">p4</font>,<font color="Olive" title="b1">P</font> holds <br/> ex <font color="Olive" title="b2">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> ex <font color="Olive" title="b3">q1</font>, <font color="Olive" title="b4">q2</font>, <font color="Olive" title="b5">q3</font>, <font color="Olive" title="b6">q4</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 <br/>( <font color="Olive" title="b2">f</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  &amp; (  for <font color="Olive" title="b7">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> holds  <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b7">q</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><font color="Olive" title="b7">q</font></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> ) &amp; <font color="Olive" title="b3">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">p1</font> &amp; <font color="Olive" title="b4">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p2</font> &amp; <font color="Olive" title="b5">q3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">p3</font> &amp; <font color="Olive" title="b6">q4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">p4</font> &amp; <font color="Olive" title="b3">q1</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b3">q1</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b4">q2</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b4">q2</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b5">q3</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b5">q3</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b6">q4</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b6">q4</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b3">q1</font>,<font color="Olive" title="b4">q2</font>,<font color="Olive" title="b1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b4">q2</font>,<font color="Olive" title="b5">q3</font>,<font color="Olive" title="b1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b5">q3</font>,<font color="Olive" title="b6">q4</font>,<font color="Olive" title="b1">P</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">P</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</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" 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="c5">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">p</font> where <font color="Olive" title="b1">p</font> is   <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> : <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><font color="Olive" title="b1">p</font></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 </span> } </span>  &amp; <font color="Maroon" title="c4">p4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c5">P</font> implies  ex <font color="Olive" title="b1">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font>, <font color="Olive" title="b4">q3</font>, <font color="Olive" title="b5">q4</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 <br/>( <font color="Olive" title="b1">f</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  &amp; (  for <font color="Olive" title="b6">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> holds  <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">q</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><font color="Olive" title="b6">q</font></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> ) &amp; <font color="Olive" title="b2">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">p1</font> &amp; <font color="Olive" title="b3">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p2</font> &amp; <font color="Olive" title="b4">q3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">p3</font> &amp; <font color="Olive" title="b5">q4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">p4</font> &amp; <font color="Olive" title="b2">q1</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b2">q1</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b3">q2</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b3">q2</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b4">q3</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b4">q3</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b5">q4</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b5">q4</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b2">q1</font>,<font color="Olive" title="b3">q2</font>,<font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b3">q2</font>,<font color="Olive" title="b4">q3</font>,<font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b4">q3</font>,<font color="Olive" title="b5">q4</font>,<font color="Maroon" title="c5">P</font> ) )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:67"/><span class="lab"><font color="Green" title="E62">A1</font></span>: 
<font color="Maroon" title="c5">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">p</font> where <font color="Olive" title="b1">p</font> is   <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> : <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><font color="Olive" title="b1">p</font></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 </span> } </span> 
 <span class="kw">and </span><br/><a NAME="E2:67"/><span class="lab"><font color="Green" title="E63">A2</font></span>: 
<font color="Maroon" title="c4">p4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Maroon" title="c5">P</font>
 <span class="kw">and </span><br/><a NAME="E3:67"/><span class="lab"><font color="Green" title="E64">A3</font></span>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c5">P</font>
 <span class="kw">and </span><br/><a NAME="E4:67"/><span class="lab"><font color="Green" title="E65">A4</font></span>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c5">P</font>
 <span class="kw">and </span><br/><a NAME="E5:67"/><span class="lab"><font color="Green" title="E66">A5</font></span>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c5">P</font>
 ; <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">  ex <font color="Olive" title="b1">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font>, <font color="Olive" title="b4">q3</font>, <font color="Olive" title="b5">q4</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 <br/>( <font color="Olive" title="b1">f</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  &amp; (  for <font color="Olive" title="b6">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> holds  <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">q</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><font color="Olive" title="b6">q</font></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> ) &amp; <font color="Olive" title="b2">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">p1</font> &amp; <font color="Olive" title="b3">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p2</font> &amp; <font color="Olive" title="b4">q3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">p3</font> &amp; <font color="Olive" title="b5">q4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">p4</font> &amp; <font color="Olive" title="b2">q1</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b2">q1</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b3">q2</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b3">q2</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b4">q3</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b4">q3</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b5">q4</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b5">q4</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b2">q1</font>,<font color="Olive" title="b3">q2</font>,<font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b3">q2</font>,<font color="Olive" title="b4">q3</font>,<font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b4">q3</font>,<font color="Olive" title="b5">q4</font>,<font color="Maroon" title="c5">P</font> )</span><br/>

<a NAME="E6:67"/><span class="lab"><font color="Green" title="E67">A6</font></span>: 
 <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">p7</font> where <font color="Olive" title="b1">p7</font> is   <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> : ( <font color="Olive" title="b1">p7</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">P</font> &amp; <font color="Olive" title="b1">p7</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="ref" href="jgraph_5.html#T34" target="_self" onmouseover="rs('jgraph_5/T34')" onmouseout="rh()">Th34</a></span>;<br/>
<a NAME="E7:67"/><span class="lab"><font color="Green" title="E68">A7</font></span>: 
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Maroon" title="c5">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="ref" href="jgraph_5.html#T29" target="_self" onmouseover="rs('jgraph_5/T29')" onmouseout="rh()">Th29</a></span>;<br/>
<a NAME="E8:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A8</font></span>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Maroon" title="c5">P</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T52" onmouseover="rs('euclid/T52')" onmouseout="rh()">EUCLID:52</a></span>;<br/>
<a NAME="E9:67"/><span class="lab"><font color="Green" title="E70">A9</font></span>: 
<font color="Maroon" title="c5">P</font> is  <a href="topreal2.html#V1" title="TOPREAL2:attr.1">being_simple_closed_curve</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="ref" href="jgraph_3.html#T26" onmouseover="rs('jgraph_3/T26')" onmouseout="rh()">JGRAPH_3:26</a></span>;<br/>
<a NAME="E10:67"/><span class="kw">then </span>
<font color="Maroon" title="c4">p4</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E66">A5</font></span></a>, <a class="ref" href="jordan7.html#T5" onmouseover="rs('jordan7/T5')" onmouseout="rh()">JORDAN7:5</a></span>;<br/>
<a NAME="E11:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A10</font></span>: 
<font color="Maroon" title="c4">p4</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="txt" href="#E6:67"><span class="lab"><font color="Green" title="E67">A6</font></span></a>, <a class="txt" href="#E8:67"><span class="lab"><font color="Green" title="E69">A8</font></span></a></span>;<br/>
<a NAME="E12:67"/><span class="lab"><font color="Green" title="E72">A11</font></span>: 
 <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Maroon" title="c5">P</font>, <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:67"><span class="lab"><font color="Green" title="E70">A9</font></span></a>, <a class="ref" href="jordan6.html#D8" onmouseover="rs('jordan6/D8')" onmouseout="rh()">JORDAN6:def 8</a></span>;<br/>
<a NAME="E13:67"/><span class="lab"><font color="Green" title="E73">A12</font></span>: 
<font color="Maroon" title="c3">p3</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E66">A5</font></span></a>, <a class="txt" href="#E11:67"><span class="lab"><font color="Green" title="E71">A10</font></span></a>, <a class="ref" href="jgraph_5.html#T44" target="_self" onmouseover="rs('jgraph_5/T44')" onmouseout="rh()">Th44</a></span>;<br/>
<a NAME="E14:67"/><span class="kw">then </span>
 <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c3">p3</font>, <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font>, <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Maroon" title="c5">P</font>, <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="txt" href="#E12:67"><span class="lab"><font color="Green" title="E72">A11</font></span></a>, <a class="ref" href="jordan5c.html#T10" onmouseover="rs('jordan5c/T10')" onmouseout="rh()">JORDAN5C:10</a></span>;<br/>
<a NAME="E15:67"/><span class="kw">then </span>
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c3">p3</font>,<font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:67"><span class="lab"><font color="Green" title="E71">A10</font></span></a>, <a class="txt" href="#E13:67"><span class="lab"><font color="Green" title="E73">A12</font></span></a></span>;<br/>
<a NAME="E16:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A13</font></span>: 
<font color="Maroon" title="c3">p3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E66">A5</font></span></a>, <a class="ref" href="jgraph_3.html#T26" onmouseover="rs('jgraph_3/T26')" onmouseout="rh()">JGRAPH_3:26</a>, <a class="ref" href="jordan6.html#T57" onmouseover="rs('jordan6/T57')" onmouseout="rh()">JORDAN6:57</a></span>;<br/>
<a NAME="E17:67"/><span class="lab"><font color="Green" title="E75">A14</font></span>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E65">A4</font></span></a>, <a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E66">A5</font></span></a>, <a class="ref" href="jgraph_3.html#T26" onmouseover="rs('jgraph_3/T26')" onmouseout="rh()">JGRAPH_3:26</a>, <a class="ref" href="jordan6.html#T58" onmouseover="rs('jordan6/T58')" onmouseout="rh()">JORDAN6:58</a></span>;<br/>
<a NAME="E18:67"/><span class="lab"><font color="Green" title="E76">A15</font></span>: 
<font color="Maroon" title="c2">p2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E65">A4</font></span></a>, <a class="txt" href="#E13:67"><span class="lab"><font color="Green" title="E73">A12</font></span></a>, <a class="ref" href="jgraph_5.html#T44" target="_self" onmouseover="rs('jgraph_5/T44')" onmouseout="rh()">Th44</a></span>;<br/>
<a NAME="E19:67"/><span class="kw">then </span>
 <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c2">p2</font>, <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font>, <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Maroon" title="c5">P</font>, <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="txt" href="#E12:67"><span class="lab"><font color="Green" title="E72">A11</font></span></a>, <a class="ref" href="jordan5c.html#T10" onmouseover="rs('jordan5c/T10')" onmouseout="rh()">JORDAN5C:10</a></span>;<br/>
<a NAME="E20:67"/><span class="kw">then </span>
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:67"><span class="lab"><font color="Green" title="E71">A10</font></span></a>, <a class="txt" href="#E18:67"><span class="lab"><font color="Green" title="E76">A15</font></span></a></span>;<br/>
<a NAME="E21:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A16</font></span>: 
<font color="Maroon" title="c2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="txt" href="#E17:67"><span class="lab"><font color="Green" title="E75">A14</font></span></a>, <a class="ref" href="jgraph_3.html#T26" onmouseover="rs('jgraph_3/T26')" onmouseout="rh()">JGRAPH_3:26</a>, <a class="ref" href="jordan6.html#T57" onmouseover="rs('jordan6/T57')" onmouseout="rh()">JORDAN6:57</a></span>;<br/>
<a NAME="E22:67"/><span class="lab"><font color="Green" title="E78">A17</font></span>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Maroon" title="c5">P</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:67"><span class="lab"><font color="Green" title="E68">A7</font></span></a>, <a class="ref" href="euclid.html#T52" onmouseover="rs('euclid/T52')" onmouseout="rh()">EUCLID:52</a></span>;<br/>
<a NAME="E23:67"/><span class="lab"><font color="Green" title="E79">A18</font></span>: 
<font color="Maroon" title="c1">p1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E64">A3</font></span></a>, <a class="txt" href="#E18:67"><span class="lab"><font color="Green" title="E76">A15</font></span></a>, <a class="ref" href="jgraph_5.html#T44" target="_self" onmouseover="rs('jgraph_5/T44')" onmouseout="rh()">Th44</a></span>;<br/>
<a NAME="E24:67"/><span class="kw">then </span>
 <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c1">p1</font>, <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Maroon" title="c5">P</font>, <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Maroon" title="c5">P</font>, <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="txt" href="#E12:67"><span class="lab"><font color="Green" title="E72">A11</font></span></a>, <a class="ref" href="jordan5c.html#T10" onmouseover="rs('jordan5c/T10')" onmouseout="rh()">JORDAN5C:10</a></span>;<br/>
<a NAME="E25:67"/><span class="kw">then </span>
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">p4</font>,<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:67"><span class="lab"><font color="Green" title="E71">A10</font></span></a>, <a class="txt" href="#E23:67"><span class="lab"><font color="Green" title="E79">A18</font></span></a></span>;<br/>
<a NAME="E26:67"/><span class="kw">then </span>
<font color="Maroon" title="c1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E64">A3</font></span></a>, <a class="txt" href="#E21:67"><span class="lab"><font color="Green" title="E77">A16</font></span></a>, <a class="ref" href="jgraph_3.html#T26" onmouseover="rs('jgraph_3/T26')" onmouseout="rh()">JGRAPH_3:26</a>, <a class="ref" href="jordan6.html#T57" onmouseover="rs('jordan6/T57')" onmouseout="rh()">JORDAN6:57</a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:67"/>
 ex <font color="Olive" title="b1">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> ex <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font>, <font color="Olive" title="b4">q3</font>, <font color="Olive" title="b5">q4</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 <br/>( <font color="Olive" title="b1">f</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  &amp; (  for <font color="Olive" title="b6">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> holds  <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">q</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><font color="Olive" title="b6">q</font></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> ) &amp; <font color="Olive" title="b2">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">p1</font> &amp; <font color="Olive" title="b3">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p2</font> &amp; <font color="Olive" title="b4">q3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">p3</font> &amp; <font color="Olive" title="b5">q4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">p4</font> &amp; <font color="Olive" title="b2">q1</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b2">q1</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b3">q2</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b3">q2</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b4">q3</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b4">q3</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b5">q4</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b5">q4</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b2">q1</font>,<font color="Olive" title="b3">q2</font>,<font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b3">q2</font>,<font color="Olive" title="b4">q3</font>,<font color="Maroon" title="c5">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Olive" title="b4">q3</font>,<font color="Olive" title="b5">q4</font>,<font color="Maroon" title="c5">P</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E64">A3</font></span></a>, <a class="txt" href="#E22:67"><span class="lab"><font color="Green" title="E78">A17</font></span></a>, <a class="txt" href="#E8:67"><span class="lab"><font color="Green" title="E69">A8</font></span></a>, <a class="txt" href="#E16:67"><span class="lab"><font color="Green" title="E74">A13</font></span></a>, <a class="txt" href="#E21:67"><span class="lab"><font color="Green" title="E77">A16</font></span></a>, <a class="ref" href="jgraph_5.html#T59" target="_self" onmouseover="rs('jgraph_5/T59')" onmouseout="rh()">Th59</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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