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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>, <font color="Maroon">c<sub>5</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font>;<br/>









<b>assume </b><a NAME="E1:16"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="euclid_4.html#K2" target="_self">Line</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>6</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E3:16"/><i><font color="Green">E12</font></i>: 
<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#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/>
<b>assume </b><a NAME="E4:16"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="euclid_4.html#K2" target="_self">Line</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>7</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E6:16"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>5</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>7</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:16_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="euclid_4.html#K2" target="_self">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E3:16_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>8</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>9</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 ;<br/><font color="Maroon">c<sub>8</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>9</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<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#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <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>9</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="euclid.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="euclid_4.html#E3:16"><i><font color="Green">E12</font></i></a>, <a class="txt" href="euclid_4.html#E6:16"><i><font color="Green">E13</font></i></a>, <a class="txt" href="euclid_4.html#E3:16_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="euclid_4.html#T6" target="_self">Th6</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>9</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<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#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <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>9</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T6" target="_self">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <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>9</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T4" target="_self">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T4" target="_self">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="euclid.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T4" target="_self">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T4" target="_self">Th4</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>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="euclid_4.html#E13"><i><font color="Green">Lemma10</font></i></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>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="euclid_4.html#E13"><i><font color="Green">Lemma10</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="euclid_4.html#E13"><i><font color="Green">Lemma10</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T7" target="_self">Th7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_4.html#T7" target="_self">Th7</a></i>
;<br/><b>hence </b><a NAME="E5:16_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="euclid_4.html#K2" target="_self">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:16"/>
 <a href="euclid_4.html#K2" target="_self">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a>  <a href="euclid_4.html#K2" target="_self">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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