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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">q1</font>, <font color="Maroon" title="c4">q2</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="jordan3.html#R2" title="JORDAN3:pred.2">LE</a> <font color="Maroon" title="c3">q1</font>,<font color="Maroon" title="c4">q2</font>,<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font> &amp;  <a href="jordan3.html#R2" title="JORDAN3:pred.2">LE</a> <font color="Maroon" title="c4">q2</font>,<font color="Maroon" title="c3">q1</font>,<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font> implies <font color="Maroon" title="c3">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q2</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="E29">A1</font></span>: 
 <a href="jordan3.html#R2" title="JORDAN3:pred.2">LE</a> <font color="Maroon" title="c3">q1</font>,<font color="Maroon" title="c4">q2</font>,<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>
 <span class="kw">and </span><br/><a NAME="E2:67"/><span class="lab"><font color="Green" title="E30">A2</font></span>: 
 <a href="jordan3.html#R2" title="JORDAN3:pred.2">LE</a> <font color="Maroon" title="c4">q2</font>,<font color="Maroon" title="c3">q1</font>,<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q2</font></span><br/>

<a NAME="E3:67"/>
<font color="Maroon" title="c3">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="jordan3.html#D6" target="_self" title="JORDAN3:def.6">Def6</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">r1</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E5:67"/><span class="lab"><font color="Green" title="E31">A3</font></span>: 
<font color="Maroon" title="c3">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">r1</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c1">p1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">r1</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">p2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E6:67"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">r1</font>
 <span class="kw">and </span><br/><a NAME="E7:67"/><span class="lab"><font color="Green" title="E33">A5</font></span>: 
<font color="Maroon" title="c5">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 ;<br/>
<a NAME="E8:67"/>
<font color="Maroon" title="c4">q2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="jordan3.html#D6" target="_self" title="JORDAN3:def.6">Def6</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">r2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E10:67"/><span class="lab"><font color="Green" title="E34">A6</font></span>: 
<font color="Maroon" title="c4">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c6">r2</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c1">p1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">r2</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c2">p2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E11:67"/><span class="lab"><font color="Green" title="E35">A7</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">r2</font>
 <span class="kw">and </span><br/><a NAME="E12:67"/><span class="lab"><font color="Green" title="E36">A8</font></span>: 
<font color="Maroon" title="c6">r2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 ;<br/>
<a NAME="E13:67"/><span class="lab"><font color="Green" title="E37">A9</font></span>: 
<font color="Maroon" title="c6">r2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">r1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="txt" href="#E6:67"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E7:67"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E10:67"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E12:67"><span class="lab"><font color="Green" title="E36">A8</font></span></a>, <a class="ref" href="jordan3.html#D6" target="_self" title="JORDAN3:def.6">Def6</a></span>;<br/>
<a NAME="E14:67"/>
<font color="Maroon" title="c5">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">r2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="txt" href="#E7:67"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E10:67"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E11:67"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="txt" href="#E12:67"><span class="lab"><font color="Green" title="E36">A8</font></span></a>, <a class="ref" href="jordan3.html#D6" target="_self" title="JORDAN3:def.6">Def6</a></span>;<br/>
<a NAME="E15:67"/><span class="kw">then </span>
<font color="Maroon" title="c5">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">r2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:67"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:67"/>
<font color="Maroon" title="c3">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="txt" href="#E10:67"><span class="lab"><font color="Green" title="E34">A6</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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