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<b>let </b><font color="Maroon" title="c1">P</font> be   <a href="topreal2.html#NM1" title="TOPREAL2:NM.1">Simple_closed_curve</a>; <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">b</font>, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">d</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="Olive" title="b1">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">c</font> &amp; <font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> holds <br/> ex <font color="Olive" title="b5">e</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="b5">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">b</font> &amp; <font color="Olive" title="b5">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">c</font> &amp; <font color="Olive" title="b1">b</font>,<font color="Olive" title="b5">e</font>,<font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/><b>let </b><font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">d</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="c2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> implies  ex <font color="Olive" title="b1">e</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">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> ) )</span><br/>









<b>assume </b><b>that </b><br/><a NAME="E1:17"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font>
 <b>and </b><br/><a NAME="E2:17"/><i><font color="Green" title="E7">A2</font></i>: 
( (  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c1">P</font> ) or (  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c1">P</font> ) or (  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">P</font> ) or (  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">P</font> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="jordan17.html#D1" target="_self" title="JORDAN17:def.1">JORDAN17:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">e</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">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:17_1"/>
( (  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c1">P</font> ) or (  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c1">P</font> ) or (  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">P</font> ) or (  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">P</font> ) )
 </span><b>by </b><i><a class="txt" href="jordan17.html#E2:17"><i><font color="Green" title="E7">A2</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1"><b>suppose </b></a><a NAME="E1:17_1_1"/><i><font color="Green" title="E8">A3</font></i>: 
(  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c1">P</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">e</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">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c6">e</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><b> such that </b><br/><a NAME="E3:17_1_1"/><i><font color="Green" title="E9">A4</font></i>: 
( <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">P</font> )
 <b>by </b><i><a class="txt" href="jordan17.html#E1:17"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="jordan17.html#T8" target="_self" title="JORDAN17:th.8">Th8</a></i>;<br/><b>take </b>
<font color="Maroon" title="c6">e</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/><b>thus </b><a NAME="E4:17_1_1"/>
( <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )
 <b>by </b><i><a class="txt" href="jordan17.html#E1:17_1_1"><i><font color="Green" title="E8">A3</font></i></a>, <a class="txt" href="jordan17.html#E3:17_1_1"><i><font color="Green" title="E9">A4</font></i></a>, <a class="ref" href="jordan17.html#D1" target="_self" title="JORDAN17:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_2"><b>suppose </b></a><a NAME="E1:17_1_2"/><i><font color="Green" title="E8">A5</font></i>: 
(  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c1">P</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">e</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">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c6">e</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><b> such that </b><br/><a NAME="E3:17_1_2"/><i><font color="Green" title="E9">A6</font></i>: 
( <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">P</font> )
 <b>by </b><i><a class="txt" href="jordan17.html#E1:17"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="jordan17.html#T8" target="_self" title="JORDAN17:th.8">Th8</a></i>;<br/><b>take </b>
<font color="Maroon" title="c6">e</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/><b>thus </b><a NAME="E4:17_1_2"/>
( <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )
 <b>by </b><i><a class="txt" href="jordan17.html#E1:17_1_2"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="jordan17.html#E3:17_1_2"><i><font color="Green" title="E9">A6</font></i></a>, <a class="ref" href="jordan17.html#D1" target="_self" title="JORDAN17:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:17_1_3"/><i><font color="Green" title="E8">A7</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c1">P</font>
 <b>and </b><br/><a NAME="E2:17_1_3"/><i><font color="Green" title="E9">A8</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c1">P</font>
 <b>and </b><br/><a NAME="E3:17_1_3"/><i><font color="Green" title="E10">A9</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">e</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">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/><div class="add"><b>thus </b><a NAME="E4:17_1_3"/>
 ex <font color="Olive" title="b1">e</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">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_3_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_1_3_1"/><i><font color="Green" title="E11">A10</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">P</font>
 
<b>by </b><i><a class="txt" href="jordan17.html#E2:17_1_3"><i><font color="Green" title="E9">A8</font></i></a>, <a class="txt" href="jordan17.html#E3:17_1_3"><i><font color="Green" title="E10">A9</font></i></a>, <a class="ref" href="jordan6.html#T73" title="JORDAN6:th.73">JORDAN6:73</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:17_1_3_1_1"/>
( <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">P</font> or <font color="Maroon" title="c3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">P</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:17_1_3_1_1_1"/><i><font color="Green" title="E12">A11</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">e</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">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/><div class="add"><a NAME="E2:17_1_3_1_1_1"/>
<font color="Maroon" title="c2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font>
 <b>by </b><i><a class="txt" href="jordan17.html#E3:17_1_3"><i><font color="Green" title="E10">A9</font></i></a>, <a class="ref" href="jordan7.html#T5" title="JORDAN7:th.5">JORDAN7:5</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">e</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><b> such that </b><br/><a NAME="E4:17_1_3_1_1_1"/><i><font color="Green" title="E13">A12</font></i>: 
<font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font>
 <b>and </b><br/><a NAME="E5:17_1_3_1_1_1"/><i><font color="Green" title="E14">A13</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c1">P</font>
 <b>by </b><i><a class="ref" href="jordan17.html#T7" target="_self" title="JORDAN17:th.7">Th7</a></i>;<br/><b>take </b>
<font color="Maroon" title="c6">e</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/><b>thus </b><a NAME="E6:17_1_3_1_1_1"/>
<font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font>
 <b>by </b><i><a class="txt" href="jordan17.html#E4:17_1_3_1_1_1"><i><font color="Green" title="E13">A12</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/><b>thus </b><a NAME="E7:17_1_3_1_1_1"/>
<font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="txt" href="jordan17.html#E1:17"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="jordan17.html#E1:17_1_3_1_1_1"><i><font color="Green" title="E12">A11</font></i></a>, <a class="txt" href="jordan17.html#E5:17_1_3_1_1_1"><i><font color="Green" title="E14">A13</font></i></a>, <a class="ref" href="jordan7.html#T2" title="JORDAN7:th.2">JORDAN7:2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font></span><br/><b>thus </b><a NAME="E8:17_1_3_1_1_1"/>
<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font>
 <b>by </b><i><a class="txt" href="jordan17.html#E1:17_1_3"><i><font color="Green" title="E8">A7</font></i></a>, <a class="txt" href="jordan17.html#E1:17_1_3_1"><i><font color="Green" title="E11">A10</font></i></a>, <a class="txt" href="jordan17.html#E5:17_1_3_1_1_1"><i><font color="Green" title="E14">A13</font></i></a>, <a class="ref" href="jordan17.html#D1" target="_self" title="JORDAN17:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:17_1_3_1_1_2"/><i><font color="Green" title="E12">A14</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">e</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">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/><div class="add"><b>take </b><font color="Maroon" title="c6">e</font> =  <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">W-min</a> <font color="Maroon" title="c1">P</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/><a NAME="E2:17_1_3_1_1_2"/>
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font>
 <b>by </b><i><a class="txt" href="jordan17.html#E1:17_1_3"><i><font color="Green" title="E8">A7</font></i></a>, <a class="ref" href="jordan7.html#T5" title="JORDAN7:th.5">JORDAN7:5</a></i>;<br/><a NAME="E3:17_1_3_1_1_2"/><b>then </b><i><font color="Green" title="E13">A15</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">P</font>
 <b>by </b><i><a class="ref" href="jordan7.html#T3" title="JORDAN7:th.3">JORDAN7:3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_3_1_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_1_3_1_1_2_1"/><i><font color="Green" title="E14">A16</font></i>: 
<font color="Maroon" title="c6">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:17_1_3_1_1_2_1"/>
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c1">P</font>
 <b>by </b><i><a class="txt" href="jordan17.html#E1:17_1_3"><i><font color="Green" title="E8">A7</font></i></a>, <a class="txt" href="jordan17.html#E2:17_1_3"><i><font color="Green" title="E9">A8</font></i></a>, <a class="ref" href="jordan6.html#T73" title="JORDAN6:th.73">JORDAN6:73</a></i>;<br/><a NAME="E3:17_1_3_1_1_2_1"/><b>then </b>
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">P</font>
 <b>by </b><i><a class="txt" href="jordan17.html#E3:17_1_3"><i><font color="Green" title="E10">A9</font></i></a>, <a class="ref" href="jordan6.html#T73" title="JORDAN6:th.73">JORDAN6:73</a></i>;<br/><b>hence </b><a NAME="E4:17_1_3_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan17.html#E1:17"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="jordan17.html#E3:17_1_3_1_1_2"><i><font color="Green" title="E13">A15</font></i></a>, <a class="txt" href="jordan17.html#E1:17_1_3_1_1_2_1"><i><font color="Green" title="E14">A16</font></i></a>, <a class="ref" href="jordan6.html#T72" title="JORDAN6:th.72">JORDAN6:72</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E5:17_1_3_1_1_2"/>
<font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/><b>thus </b><a NAME="E6:17_1_3_1_1_2"/>
<font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="txt" href="jordan17.html#E1:17_1_3_1_1_2"><i><font color="Green" title="E12">A14</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font></span><br/><b>thus </b><a NAME="E7:17_1_3_1_1_2"/>
<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font>
 <b>by </b><i><a class="txt" href="jordan17.html#E1:17_1_3"><i><font color="Green" title="E8">A7</font></i></a>, <a class="txt" href="jordan17.html#E1:17_1_3_1"><i><font color="Green" title="E11">A10</font></i></a>, <a class="txt" href="jordan17.html#E3:17_1_3_1_1_2"><i><font color="Green" title="E13">A15</font></i></a>, <a class="ref" href="jordan17.html#D1" target="_self" title="JORDAN17:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_4"><b>suppose </b></a><b>that </b><a NAME="E1:17_1_4"/><i><font color="Green" title="E8">A17</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c1">P</font>
 <b>and </b><br/><a NAME="E2:17_1_4"/><i><font color="Green" title="E9">A18</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">P</font>
 <b>and </b><br/><a NAME="E3:17_1_4"/><i><font color="Green" title="E10">A19</font></i>: 
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">e</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">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/><div class="add"><b>consider </b><font color="Maroon" title="c6">e</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><b> such that </b><br/><a NAME="E5:17_1_4"/><i><font color="Green" title="E11">A20</font></i>: 
( <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c1">P</font> &amp;  <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">P</font> )
 <b>by </b><i><a class="txt" href="jordan17.html#E1:17"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="jordan17.html#E3:17_1_4"><i><font color="Green" title="E10">A19</font></i></a>, <a class="ref" href="jordan17.html#T8" target="_self" title="JORDAN17:th.8">Th8</a></i>;<br/><b>take </b>
<font color="Maroon" title="c6">e</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font> )</span><br/><b>thus </b><a NAME="E6:17_1_4"/>
( <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Maroon" title="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> )
 <b>by </b><i><a class="txt" href="jordan17.html#E5:17_1_4"><i><font color="Green" title="E11">A20</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font></span><br/><a NAME="E7:17_1_4"/>
 <a href="jordan6.html#R1" title="JORDAN6:pred.1">LE</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">P</font>
 <b>by </b><i><a class="txt" href="jordan17.html#E1:17_1_4"><i><font color="Green" title="E8">A17</font></i></a>, <a class="txt" href="jordan17.html#E2:17_1_4"><i><font color="Green" title="E9">A18</font></i></a>, <a class="ref" href="jordan6.html#T73" title="JORDAN6:th.73">JORDAN6:73</a></i>;<br/><b>hence </b><a NAME="E8:17_1_4"/>
<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="jordan17.html#R1" title="JORDAN17:pred.1">are_in_this_order_on</a> <font color="Maroon" title="c1">P</font>
 <b>by </b><i><a class="txt" href="jordan17.html#E5:17_1_4"><i><font color="Green" title="E11">A20</font></i></a>, <a class="ref" href="jordan17.html#D1" target="_self" title="JORDAN17:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
