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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="197_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:197_1_1_1"/>
( <font color="Maroon" title="c6">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or <font color="Maroon" title="c6">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="197_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:197_1_1_1_1"/>
<font color="Maroon" title="c6">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">a</font> <a href="prepower.html#K3" title="PREPOWER:func.3">#Z</a> <font color="Maroon" title="c6">i</font> is  <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a> </span><br/><div class="add"><a NAME="E2:197_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a</font> <a href="prepower.html#K3" title="PREPOWER:func.3">#Z</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <span class="p2"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><font color="Maroon" title="c6">i</font></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span></span>)</span> <a href="xcmplx_0.html#K5" title="XCMPLX_0:func.5">"</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prepower.html#D3" onmouseover="rs('prepower/D3')" onmouseout="rh()">PREPOWER:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:197_1_1_1_1"/>
<font color="Maroon" title="c5">a</font> <a href="prepower.html#K3" title="PREPOWER:func.3">#Z</a> <font color="Maroon" title="c6">i</font> is  <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="197_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:197_1_1_1_2"/>
<font color="Maroon" title="c6">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">a</font> <a href="prepower.html#K3" title="PREPOWER:func.3">#Z</a> <font color="Maroon" title="c6">i</font> is  <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a> </span><br/><div class="add"><a NAME="E2:197_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">a</font> <a href="prepower.html#K3" title="PREPOWER:func.3">#Z</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><font color="Maroon" title="c6">i</font></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prepower.html#D3" onmouseover="rs('prepower/D3')" onmouseout="rh()">PREPOWER:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:197_1_1_1_2"/>
<font color="Maroon" title="c5">a</font> <a href="prepower.html#K3" title="PREPOWER:func.3">#Z</a> <font color="Maroon" title="c6">i</font> is  <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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