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<b>let </b><font color="Maroon">x</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:21"/><i><font color="Green">E21</font></i>: 
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 ;<br/>

<a NAME="E2:21"/><b>then </b>
<font color="Maroon">x</font> <a href="square_1.html#K3">^2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="square_1.html#T75">SQUARE_1:75</a></i>;<br/>
<a NAME="E3:21"/><b>then </b>
<font color="Maroon">x</font> <a href="square_1.html#K3">^2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1
 
<b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E4:21"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K3">^2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<b>hence </b><a NAME="E5:21"/>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/>


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