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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>







<b>assume </b><a NAME="E1:44"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E3:44"/><i><font color="Green">E40</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="jgraph_1.html#T52" target="_self">Th52</a></i>;<br/>
<font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K19">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_1.html#E3:44"><i><font color="Green">E40</font></i></a>, <a class="ref" href="euclid.html#T45">EUCLID:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K19">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T30">EUCLID:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T45">EUCLID:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2">(<span class="default">1 <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T33">EUCLID:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T54">EUCLID:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K19">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T44">EUCLID:44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><a href="euclid.html#K19">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T44">EUCLID:44</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K18">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K19">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T36">EUCLID:36</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K18">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T45">EUCLID:45</a></i>
;<br/>
<b>then </b><span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> = 
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span>
<b>by </b><i><a class="ref" href="toprns_1.html#T8">TOPRNS_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span>
<b>by </b><i><a class="ref" href="toprns_1.html#T28">TOPRNS_1:28</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="real_1.html#K4">*</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span>
<b>by </b><i><a class="txt" href="jgraph_1.html#E3:44"><i><font color="Green">E40</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
;<br/>
<a NAME="E6:44"/><b>then </b><i><font color="Green">E41</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="real_1.html#K5">-</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span>
 
;<br/>
<a NAME="E7:44"/><i><font color="Green">E42</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_1.html#E3:44"><i><font color="Green">E40</font></i></a>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<a NAME="E8:44"/>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="toprns_1.html#T26">TOPRNS_1:26</a></i>;<br/>
<a NAME="E9:44"/><b>then </b><i><font color="Green">E43</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="real_1.html#K5">-</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_1.html#E6:44"><i><font color="Green">E41</font></i></a>, <a class="txt" href="jgraph_1.html#E7:44"><i><font color="Green">E42</font></i></a>, <a class="ref" href="xreal_1.html#T129">XREAL_1:129</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E11:44"/><i><font color="Green">E44</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="jgraph_1.html#E1:44"><i><font color="Green">E39</font></i></a>, <a class="ref" href="jgraph_1.html#T52" target="_self">Th52</a></i>;<br/>
<font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K19">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_1.html#E11:44"><i><font color="Green">E44</font></i></a>, <a class="ref" href="euclid.html#T45">EUCLID:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K19">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T30">EUCLID:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T45">EUCLID:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p2">(<span class="default">1 <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T33">EUCLID:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T54">EUCLID:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K19">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T44">EUCLID:44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><a href="euclid.html#K19">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T44">EUCLID:44</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K18">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><a href="euclid.html#K19">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T36">EUCLID:36</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K18">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T45">EUCLID:45</a></i>
;<br/>
<b>then </b><span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> = 
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span>
<b>by </b><i><a class="ref" href="toprns_1.html#T8">TOPRNS_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K4">*</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span>
<b>by </b><i><a class="txt" href="jgraph_1.html#E11:44"><i><font color="Green">E44</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
;<br/>
<a NAME="E14:44"/><b>then </b><i><font color="Green">E45</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="real_1.html#K5">-</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span>
 
;<br/>
<a NAME="E15:44"/><i><font color="Green">E46</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_1.html#E11:44"><i><font color="Green">E44</font></i></a>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<a NAME="E16:44"/>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="toprns_1.html#T26">TOPRNS_1:26</a></i>;<br/>
<a NAME="E17:44"/><b>then </b>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="real_1.html#K5">-</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_1.html#E14:44"><i><font color="Green">E45</font></i></a>, <a class="txt" href="jgraph_1.html#E15:44"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xreal_1.html#T129">XREAL_1:129</a></i>;<br/>
<b>hence </b><a NAME="E18:44"/>
( <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> &amp; <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> )
 <b>by </b><i><a class="txt" href="jgraph_1.html#E9:44"><i><font color="Green">E43</font></i></a>, <a class="ref" href="real_2.html#T105">REAL_2:105</a></i>;<br/>


</div>
