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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:82_1"/><i><font color="Green">E59</font></i>: 
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:82_1"/><b>then </b><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><b>thus </b><a NAME="E3:82_1"/>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="square_1.html#K6">sqrt</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E1:82_1"><i><font color="Green">E59</font></i></a>, <a class="ref" href="square_1.html#T83">SQUARE_1:83</a>, <a class="ref" href="square_1.html#T95">SQUARE_1:95</a></i>;<br/><a NAME="E4:82_1"/><b>then </b>
 <a href="square_1.html#K6">sqrt</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> 
 <b>by </b><i><a class="ref" href="square_1.html#T76">SQUARE_1:76</a></i>;<br/><b>hence </b><a NAME="E5:82_1"/>
 <a href="square_1.html#K6">sqrt</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E2:82_1"><i><font color="Green">E60</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:82_2"/><i><font color="Green">E59</font></i>: 
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 ;<br/><b>hence </b><a NAME="E2:82_2"/><i><font color="Green">E60</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="square_1.html#K6">sqrt</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="square_1.html#T82">SQUARE_1:82</a>, <a class="ref" href="square_1.html#T95">SQUARE_1:95</a></i>;<br/><b>thus </b><a NAME="E3:82_2"/>
 <a href="square_1.html#K6">sqrt</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1
 <b>by </b><i><a class="txt" href="wsierp_1.html#E1:82_2"><i><font color="Green">E59</font></i></a>, <a class="ref" href="square_1.html#T83">SQUARE_1:83</a>, <a class="ref" href="square_1.html#T95">SQUARE_1:95</a></i>;<br/><a NAME="E4:82_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="square_1.html#K3">^2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="square_1.html#K6">sqrt</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E2:82_2"><i><font color="Green">E60</font></i></a>, <a class="ref" href="square_1.html#T75">SQUARE_1:75</a></i>;<br/><b>hence </b><a NAME="E5:82_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="square_1.html#K6">sqrt</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E1:82_2"><i><font color="Green">E59</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>;<br/></div>
<b>end;</b></div>


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