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<b>let </b><font color="Maroon" title="c1">x</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>

<b>assume </b><a NAME="E1:2"/><i><font color="Green" title="E3">A1</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/>

<a NAME="E2:2"/><b>then </b><i><font color="Green" title="E4">A2</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#R</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="prepower.html#T95" title="PREPOWER:th.95">PREPOWER:95</a></i>;<br/>
<font color="Maroon" title="c1">x</font> = 
<font color="Maroon" title="c1">x</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#R</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T86" title="PREPOWER:th.86">PREPOWER:86</a>, <a class="txt" href="fdiff_7.html#E1:2"><i><font color="Green" title="E3">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span>)</span> <a href="prepower.html#K11" title="PREPOWER:func.11">#R</a> 2
<b>by </b><i><a class="ref" href="prepower.html#T105" title="PREPOWER:th.105">PREPOWER:105</a>, <a class="txt" href="fdiff_7.html#E1:2"><i><font color="Green" title="E3">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span>)</span> <a href="prepower.html#K7" title="PREPOWER:func.7">#Q</a> 2
<b>by </b><i><a class="txt" href="fdiff_7.html#E2:2"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="prepower.html#T88" title="PREPOWER:th.88">PREPOWER:88</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> 2
<b>by </b><i><a class="txt" href="fdiff_7.html#E2:2"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="power.html#T51" title="POWER:th.51">POWER:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> 
<b>by </b><i><a class="ref" href="power.html#T53" title="POWER:th.53">POWER:53</a></i>
;<br/>
<b>hence </b><a NAME="E4:2"/>
<font color="Maroon" title="c1">x</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#R</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <font color="Maroon" title="c1">x</font>
 <b>by </b><i><a class="txt" href="fdiff_7.html#E2:2"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="square_1.html#D4" title="SQUARE_1:def.4">SQUARE_1:def 4</a>, <a class="txt" href="fdiff_7.html#E1:2"><i><font color="Green" title="E3">A1</font></i></a></i>;<br/>


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